The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The original version of this article unfortunately contained an error in Equation 2. The division... more The original version of this article unfortunately contained an error in Equation 2. The division operator "/" was missing in between σ2 and e0. The corrected Equation 2 is shown below. The original article has been corrected. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. a = 1∕2(e 0 + (2 ∕e 0))
This paper discusses known mathematical equalities and inequalities found within life tables and ... more This paper discusses known mathematical equalities and inequalities found within life tables and proceeds to identify two new inequalities. The first (theorem 1) is that at any given age x, the sum of mean years lived and mean years remaining exceeds life expectancy at birth when age is greater than zero and less than the maximum lifespan. The second inequality (theorem 2) applies to the entire population and shows that the sum of mean years lived and mean years remaining exceeds life expectancy at birth. Illustrations of the two inequalities are provided as well as a discussion. Résumé Cet article examine les égalités et les inégalités mathématiques connues dans les tables de mortalité et procède à l'identification de deux nouvelles inégalités. La premiére (théorème 1) est que,à tout âge x donné, la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance lorsque l'âge est supérieur à zéro et inférieur à la durée de vie maximale. La deuxième inégalité (théorème 2) s'applique à l'ensemble de la population et montre que la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance. Des illustrations des deux inégalités sont fournies ainsi qu'une discussion. Keywords Carey's Equality Theorem. Life years lost. Life expectancy at birth. Mean years lived. mean years remaining. variance in age at death Mots-clé théoréme d'égalité de Carey. années de vie perdues. espérance de vie à la naissance. nombre d'années vécues. nombre d'années restantes. variance de l'âge au décès
1 Western Sociological Review SUMMER 1975 VGLUME 6 ARTICLES CHARLES F. CORTESE AND MICHAEL TIMBER... more 1 Western Sociological Review SUMMER 1975 VGLUME 6 ARTICLES CHARLES F. CORTESE AND MICHAEL TIMBERLAKE Toward A Theory of Selective Black Migration/3 GEORGE A. MILLER Dimensions of Bureaucracy: A Smallest Space Analysis/20 BARRY D. LEBOWITZ Issues in Concept Formation: The Case of Status Consistency/33 JOHN R. KIMBERLY Classification and Organizational Analysis the Case of Rehabilitation Organizations/47 GREG ZERSCHLING AND BARTO LOMEO J. PALlSl Rationality of Coalition Formation in the Triad/61 DAVID A. SWANSON The Division of Labor: Further Exploration in the Analysis of an Ecological Concept/72 COMMENTARY/83 BOOK REVIEWS/84
Taylor's law (TL) is a widely observed empirical pattern that relates variance to the the mean of... more Taylor's law (TL) is a widely observed empirical pattern that relates variance to the the mean of a set of non-negative measurements via an approximate power function: varianceg ≈ a × (meang) b , where g indexes the group of measurements. While widely observed, we have not found an application of TL to annualized state unemployment data. Thus, in this paper, we construct a model using TL to estimate of the variance in the 2018 annualized number of employed by state using the mean number. Our "in-sample" set consists of 38 states with 25 or more counties. We then test the model by estimating the variance in the 2018 annualized number of employed by state using the mean number. Our "out-of-sample" test set consists of the 12 states with fewer than 25 counties. Variance in the numbers of annualized unemployed by county within each state is important because it is a summary measure of how disproportionate unemployment is spread across counties. This suggests that policy-based efforts to reduce unemployment inequality among counties in a given state might better serve a state with a high mean level of county unemployment than a state with a low mean level of county unemployment because Taylor's Law shows that there is a higher level of unemployment inequality in the former than in the latter.
BackgroundCOVID-19 was first identified in Wuhan, the capital city of the province of Hubei in Ch... more BackgroundCOVID-19 was first identified in Wuhan, the capital city of the province of Hubei in China. Due to the presentation of multiple symptoms at the same time, it is clinically important to understand the probability of dying from COVID-19 vs. the probability of dying from other causes.MethodsUsing data collected in Hubei that identified by age those who died of COVID-19 or its sequelae among the infected, we constructed a life table showing the conditional probability of dying at age x from COVID-19 and its sequela among those infected. Following the relative survival perspective, we also computed corresponding data for China that matched the format of the life table we constructed from the Hubei study. We then formed ratios of the 10-year conditional portability of dying at age x from COVID-19 for the Hubei COVID-19 victims to the ten-year conditional probability of dying at age x from all non-COVID-19 causes for those not infected by COVID-19 in China as a whole.FindingsAt e...
Proceedings of the Sixth Eurostat/Unece Work Session on Demographic Projections Italian National ... more Proceedings of the Sixth Eurostat/Unece Work Session on Demographic Projections Italian National Institute of Statistics
LAQ20(1) danforth 2:59 PM Page 3 JUVENILE AGE ESTIMATION USING DIAPHYSEAL LONG BONE LENGTHS AMONG... more LAQ20(1) danforth 2:59 PM Page 3 JUVENILE AGE ESTIMATION USING DIAPHYSEAL LONG BONE LENGTHS AMONG ANCIENT MAYA POPULATIONS Marie Elaine Danforth, Gabriel D. Wrobel, Carl W. Armstrong, and David Swanson Standards for diaphyseal lengths of the femur, humerus, and tibia that can be used in juvenile age estimation for the ancient Maya are presented. It is argued that these new standards are necessary given differences in stature and limb proportion in Mesoamerican groups compared to the prehistoric North American groups upon whom the current available standards have been developed. Using data from 96 juveniles in the protohistoric Maya series from Tipu, Belize, regression equations were developed to predict age of dental development using diaphyseal lengths; all had excellent fit and statistical signifi- cance. When the equations were tested with diaphyseal lengths from other Mesoamerican populations, the results were sup- portive of such application. Se presentan los estandares de las ...
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
by Thomas K. BurchDemographic Research Monographs.Dordrecht: Springer, 2018.ISBN 978-3-319-65432-... more by Thomas K. BurchDemographic Research Monographs.Dordrecht: Springer, 2018.ISBN 978-3-319-65432-4.Softcover C$24.99, 200 pp.e-book DOI 10.1007/978-3-319-65433-1
The field of applied demography is largely driven by the quest for the knowledge required by clie... more The field of applied demography is largely driven by the quest for the knowledge required by clients, both in public and private sectors, to make good decisions within time and costs constraints. The book series, Applied Demography, provides a forum for illustrating and discussing the use of demographic methods, concepts, and perspectives in a wide range of settings-business, government, education, law, and public policy-as well as the influence of these settings on demographic methods, concepts, and perspectives. The books within the series can be used as resources for practitioners and as materials serving as case studies for pedagogical uses.
National undercount adjustment factors from the 1970 and 1980 U.S. censuses are used to prepare p... more National undercount adjustment factors from the 1970 and 1980 U.S. censuses are used to prepare population projections for Ohio, which are in turn compared with unadjusted projections. "The findings suggest that decisions concerning adjustment factors have varying effects on short-term, long-term, and strategic forecasting. These effects are particularly salient for selected age-groups and the impact on state government budget decisions typically associated with these age-groups. We recommend that the effects of alternative adjustment possibilities be examined by state demographic centers and budget offices."
Infant mortality differentials in a metropolitan aggregate of eight Ohio cities were examined for... more Infant mortality differentials in a metropolitan aggregate of eight Ohio cities were examined for the years 1979-81. The primary analytical unit was the census tract of mother's usual residence. The independent variable was defined as the percentage of low-income families in each tract at the 1980 census. Results of the analysis revealed that in spite of some very substantial declines in the overall level of infant mortality in recent decades, there continues to be a pronounced inverse association between the aggregate economic status of an area and the probability that a newborn infant will not survive the first year of life. This inverse association characterizes both males and females, whites as well as nonwhites, and it is observed during both the neonatal and postneonatal age intervals. Moreover, it is apparent that the adverse influence of a low economic status is reflected in the incidence of mortality from all major exogenous and endogenous causes. Since these two cause ...
is published in January (annual meeting abstracts), April, July, and October, by the Mississippi ... more is published in January (annual meeting abstracts), April, July, and October, by the Mississippi Academy of Sciences. Members of the Academy receive the journal as part of their regular (non-student) membership. Inquiries regarding subscriptions, availability of back issues, and address changes should be addressed to The Mississippi Academy of Sciences,
No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form ... more No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfi lming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifi cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
Population forecasting is a difficult endeavor. When it involves a "small" population, forecastin... more Population forecasting is a difficult endeavor. When it involves a "small" population, forecasting becomes even more difficult because of the lack of adequate input data to appropriately implement a technique preferred by demographers, the cohortcomponent method (CCM). Small populations also are subject to high levels of stochastic uncertainty, which can lead to substantial temporal fluctuations in size as well as mortality, fertility, and migration rates over short periods of time. When the population is further defined in terms of characteristics such as tribal membership requirements, the acquisition of relevant age-sex and component data for the discrete population adds even more difficulty because the usual data sources may not have precise data for a given tribe, especially when there is a need for long-term forecasts as is the case in disputes over water allotments. In this case study of the Hopi tribal population, I show that these problems can be overcome, resulting in reasonably accurate forecasts over a long period of time. To do this, I identify three key input data sources: (1) an historic tribal census that serves as the basis for tribal membership; (2) the Social Security Administration's life tables, which are specific to cohorts by year of birth, staring in 1900; and (3) an accurate annual record of tribal membership record that covers a time period that can be used as a benchmark once the forecast is launched from the historic tribal census. For this case study. these three data sources allow me to launch an 80 year CCM forecast of the Hopi Tribal Population from its 1937 tribal census to 2017 and conduct an ex post facto assessment of the accuracy of the forecasted total population in five-year increments from 1992 to 2017 using the annual tribal membership roll for this period; the assessment finds that the forecast matches up well with the tribal membership roll. So without adjustments, the forecast is taken out 20 years more, from 2017 to 2037. The results suggest that accurate long-term forecasts are possible using the cohort-component method for the Hopi, which, in turn, suggests that this same CCM process could be used to develop reasonably accurate long-term population forecasts of other tribes for which a tribal census was conducted that is linked to current tribal membership rolls, especially when these forecasts are required in resolving disputes over water allotments.
Both demographers and economists evaluate the accuracy of their respective forecasts with measure... more Both demographers and economists evaluate the accuracy of their respective forecasts with measures like mean square error, root mean square error, mean absolute percent error, and mean algebraic percent error. However, demographers tend to approach the issue of forecasting very differently than do economists. Two of the distinctive features of the demographic tradition are the use of the cohort-component method (instead of time-series models) and an emphasis on cross-sectional forecasts (instead of forecasts aggregated over time). From the perspective of this demographic tradition, we examine "MAPE-R" (Mean Absolute Percent Error-Rescaled), a recently developed measure of accuracy designed to overcome shortcomings noted in "MAPE" (Mean Absolute Percent Error), a measure commonly used to evaluate the accuracy of population estimates and forecasts. We show that MAPE-R can be calculated simply, thus overcoming the cumbersome calculation procedure used in its introduction and noted as a feature needing correction. We find this closed form expression for MAPE-R to be a member of the family of power mean-based accuracy measures. This enables it to be placed in relation to other members of this family, which includes HMAPE (Harmonic Mean Absolute Percent Error), GMAPE (Geometric Mean Absolute Percent Error), and MAPE. Given that MAPE-R was designed to be robust in the face of outliers, it is not surprising to find that it is a valid estimator of the median of the distribution(s) generating the absolute percent errors. Simulation studies suggest that MAPE-R is a far more efficient estimator of this median than MEDAPE (Median Absolute Percent Error). Because the Box-Cox transformation on which MAPE-R depends is known to be unstable, we suggest that this represents a line of further research into GMAPE, which, like MAPE-R, is subject neither to the shortcomings observed for MAPE nor to the instability of the Box-Cox transformation. While further lines of research are called for, nothing in our examination of MAPE-R here rules out its use. It also meets the National Research Council's major criteria as a summary measure of accuracy. It is subject to some cautions, but these are no more restrictive than those affecting other accuracy measures, many of which are widely used and have been for some years.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The original version of this article unfortunately contained an error in Equation 2. The division... more The original version of this article unfortunately contained an error in Equation 2. The division operator "/" was missing in between σ2 and e0. The corrected Equation 2 is shown below. The original article has been corrected. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. a = 1∕2(e 0 + (2 ∕e 0))
This paper discusses known mathematical equalities and inequalities found within life tables and ... more This paper discusses known mathematical equalities and inequalities found within life tables and proceeds to identify two new inequalities. The first (theorem 1) is that at any given age x, the sum of mean years lived and mean years remaining exceeds life expectancy at birth when age is greater than zero and less than the maximum lifespan. The second inequality (theorem 2) applies to the entire population and shows that the sum of mean years lived and mean years remaining exceeds life expectancy at birth. Illustrations of the two inequalities are provided as well as a discussion. Résumé Cet article examine les égalités et les inégalités mathématiques connues dans les tables de mortalité et procède à l'identification de deux nouvelles inégalités. La premiére (théorème 1) est que,à tout âge x donné, la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance lorsque l'âge est supérieur à zéro et inférieur à la durée de vie maximale. La deuxième inégalité (théorème 2) s'applique à l'ensemble de la population et montre que la somme d'années moyennes vécues et d'années moyennes restantes dépasse l'espérance de vie à la naissance. Des illustrations des deux inégalités sont fournies ainsi qu'une discussion. Keywords Carey's Equality Theorem. Life years lost. Life expectancy at birth. Mean years lived. mean years remaining. variance in age at death Mots-clé théoréme d'égalité de Carey. années de vie perdues. espérance de vie à la naissance. nombre d'années vécues. nombre d'années restantes. variance de l'âge au décès
1 Western Sociological Review SUMMER 1975 VGLUME 6 ARTICLES CHARLES F. CORTESE AND MICHAEL TIMBER... more 1 Western Sociological Review SUMMER 1975 VGLUME 6 ARTICLES CHARLES F. CORTESE AND MICHAEL TIMBERLAKE Toward A Theory of Selective Black Migration/3 GEORGE A. MILLER Dimensions of Bureaucracy: A Smallest Space Analysis/20 BARRY D. LEBOWITZ Issues in Concept Formation: The Case of Status Consistency/33 JOHN R. KIMBERLY Classification and Organizational Analysis the Case of Rehabilitation Organizations/47 GREG ZERSCHLING AND BARTO LOMEO J. PALlSl Rationality of Coalition Formation in the Triad/61 DAVID A. SWANSON The Division of Labor: Further Exploration in the Analysis of an Ecological Concept/72 COMMENTARY/83 BOOK REVIEWS/84
Taylor's law (TL) is a widely observed empirical pattern that relates variance to the the mean of... more Taylor's law (TL) is a widely observed empirical pattern that relates variance to the the mean of a set of non-negative measurements via an approximate power function: varianceg ≈ a × (meang) b , where g indexes the group of measurements. While widely observed, we have not found an application of TL to annualized state unemployment data. Thus, in this paper, we construct a model using TL to estimate of the variance in the 2018 annualized number of employed by state using the mean number. Our "in-sample" set consists of 38 states with 25 or more counties. We then test the model by estimating the variance in the 2018 annualized number of employed by state using the mean number. Our "out-of-sample" test set consists of the 12 states with fewer than 25 counties. Variance in the numbers of annualized unemployed by county within each state is important because it is a summary measure of how disproportionate unemployment is spread across counties. This suggests that policy-based efforts to reduce unemployment inequality among counties in a given state might better serve a state with a high mean level of county unemployment than a state with a low mean level of county unemployment because Taylor's Law shows that there is a higher level of unemployment inequality in the former than in the latter.
BackgroundCOVID-19 was first identified in Wuhan, the capital city of the province of Hubei in Ch... more BackgroundCOVID-19 was first identified in Wuhan, the capital city of the province of Hubei in China. Due to the presentation of multiple symptoms at the same time, it is clinically important to understand the probability of dying from COVID-19 vs. the probability of dying from other causes.MethodsUsing data collected in Hubei that identified by age those who died of COVID-19 or its sequelae among the infected, we constructed a life table showing the conditional probability of dying at age x from COVID-19 and its sequela among those infected. Following the relative survival perspective, we also computed corresponding data for China that matched the format of the life table we constructed from the Hubei study. We then formed ratios of the 10-year conditional portability of dying at age x from COVID-19 for the Hubei COVID-19 victims to the ten-year conditional probability of dying at age x from all non-COVID-19 causes for those not infected by COVID-19 in China as a whole.FindingsAt e...
Proceedings of the Sixth Eurostat/Unece Work Session on Demographic Projections Italian National ... more Proceedings of the Sixth Eurostat/Unece Work Session on Demographic Projections Italian National Institute of Statistics
LAQ20(1) danforth 2:59 PM Page 3 JUVENILE AGE ESTIMATION USING DIAPHYSEAL LONG BONE LENGTHS AMONG... more LAQ20(1) danforth 2:59 PM Page 3 JUVENILE AGE ESTIMATION USING DIAPHYSEAL LONG BONE LENGTHS AMONG ANCIENT MAYA POPULATIONS Marie Elaine Danforth, Gabriel D. Wrobel, Carl W. Armstrong, and David Swanson Standards for diaphyseal lengths of the femur, humerus, and tibia that can be used in juvenile age estimation for the ancient Maya are presented. It is argued that these new standards are necessary given differences in stature and limb proportion in Mesoamerican groups compared to the prehistoric North American groups upon whom the current available standards have been developed. Using data from 96 juveniles in the protohistoric Maya series from Tipu, Belize, regression equations were developed to predict age of dental development using diaphyseal lengths; all had excellent fit and statistical signifi- cance. When the equations were tested with diaphyseal lengths from other Mesoamerican populations, the results were sup- portive of such application. Se presentan los estandares de las ...
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
by Thomas K. BurchDemographic Research Monographs.Dordrecht: Springer, 2018.ISBN 978-3-319-65432-... more by Thomas K. BurchDemographic Research Monographs.Dordrecht: Springer, 2018.ISBN 978-3-319-65432-4.Softcover C$24.99, 200 pp.e-book DOI 10.1007/978-3-319-65433-1
The field of applied demography is largely driven by the quest for the knowledge required by clie... more The field of applied demography is largely driven by the quest for the knowledge required by clients, both in public and private sectors, to make good decisions within time and costs constraints. The book series, Applied Demography, provides a forum for illustrating and discussing the use of demographic methods, concepts, and perspectives in a wide range of settings-business, government, education, law, and public policy-as well as the influence of these settings on demographic methods, concepts, and perspectives. The books within the series can be used as resources for practitioners and as materials serving as case studies for pedagogical uses.
National undercount adjustment factors from the 1970 and 1980 U.S. censuses are used to prepare p... more National undercount adjustment factors from the 1970 and 1980 U.S. censuses are used to prepare population projections for Ohio, which are in turn compared with unadjusted projections. "The findings suggest that decisions concerning adjustment factors have varying effects on short-term, long-term, and strategic forecasting. These effects are particularly salient for selected age-groups and the impact on state government budget decisions typically associated with these age-groups. We recommend that the effects of alternative adjustment possibilities be examined by state demographic centers and budget offices."
Infant mortality differentials in a metropolitan aggregate of eight Ohio cities were examined for... more Infant mortality differentials in a metropolitan aggregate of eight Ohio cities were examined for the years 1979-81. The primary analytical unit was the census tract of mother's usual residence. The independent variable was defined as the percentage of low-income families in each tract at the 1980 census. Results of the analysis revealed that in spite of some very substantial declines in the overall level of infant mortality in recent decades, there continues to be a pronounced inverse association between the aggregate economic status of an area and the probability that a newborn infant will not survive the first year of life. This inverse association characterizes both males and females, whites as well as nonwhites, and it is observed during both the neonatal and postneonatal age intervals. Moreover, it is apparent that the adverse influence of a low economic status is reflected in the incidence of mortality from all major exogenous and endogenous causes. Since these two cause ...
is published in January (annual meeting abstracts), April, July, and October, by the Mississippi ... more is published in January (annual meeting abstracts), April, July, and October, by the Mississippi Academy of Sciences. Members of the Academy receive the journal as part of their regular (non-student) membership. Inquiries regarding subscriptions, availability of back issues, and address changes should be addressed to The Mississippi Academy of Sciences,
No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form ... more No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfi lming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifi cally for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
Population forecasting is a difficult endeavor. When it involves a "small" population, forecastin... more Population forecasting is a difficult endeavor. When it involves a "small" population, forecasting becomes even more difficult because of the lack of adequate input data to appropriately implement a technique preferred by demographers, the cohortcomponent method (CCM). Small populations also are subject to high levels of stochastic uncertainty, which can lead to substantial temporal fluctuations in size as well as mortality, fertility, and migration rates over short periods of time. When the population is further defined in terms of characteristics such as tribal membership requirements, the acquisition of relevant age-sex and component data for the discrete population adds even more difficulty because the usual data sources may not have precise data for a given tribe, especially when there is a need for long-term forecasts as is the case in disputes over water allotments. In this case study of the Hopi tribal population, I show that these problems can be overcome, resulting in reasonably accurate forecasts over a long period of time. To do this, I identify three key input data sources: (1) an historic tribal census that serves as the basis for tribal membership; (2) the Social Security Administration's life tables, which are specific to cohorts by year of birth, staring in 1900; and (3) an accurate annual record of tribal membership record that covers a time period that can be used as a benchmark once the forecast is launched from the historic tribal census. For this case study. these three data sources allow me to launch an 80 year CCM forecast of the Hopi Tribal Population from its 1937 tribal census to 2017 and conduct an ex post facto assessment of the accuracy of the forecasted total population in five-year increments from 1992 to 2017 using the annual tribal membership roll for this period; the assessment finds that the forecast matches up well with the tribal membership roll. So without adjustments, the forecast is taken out 20 years more, from 2017 to 2037. The results suggest that accurate long-term forecasts are possible using the cohort-component method for the Hopi, which, in turn, suggests that this same CCM process could be used to develop reasonably accurate long-term population forecasts of other tribes for which a tribal census was conducted that is linked to current tribal membership rolls, especially when these forecasts are required in resolving disputes over water allotments.
Both demographers and economists evaluate the accuracy of their respective forecasts with measure... more Both demographers and economists evaluate the accuracy of their respective forecasts with measures like mean square error, root mean square error, mean absolute percent error, and mean algebraic percent error. However, demographers tend to approach the issue of forecasting very differently than do economists. Two of the distinctive features of the demographic tradition are the use of the cohort-component method (instead of time-series models) and an emphasis on cross-sectional forecasts (instead of forecasts aggregated over time). From the perspective of this demographic tradition, we examine "MAPE-R" (Mean Absolute Percent Error-Rescaled), a recently developed measure of accuracy designed to overcome shortcomings noted in "MAPE" (Mean Absolute Percent Error), a measure commonly used to evaluate the accuracy of population estimates and forecasts. We show that MAPE-R can be calculated simply, thus overcoming the cumbersome calculation procedure used in its introduction and noted as a feature needing correction. We find this closed form expression for MAPE-R to be a member of the family of power mean-based accuracy measures. This enables it to be placed in relation to other members of this family, which includes HMAPE (Harmonic Mean Absolute Percent Error), GMAPE (Geometric Mean Absolute Percent Error), and MAPE. Given that MAPE-R was designed to be robust in the face of outliers, it is not surprising to find that it is a valid estimator of the median of the distribution(s) generating the absolute percent errors. Simulation studies suggest that MAPE-R is a far more efficient estimator of this median than MEDAPE (Median Absolute Percent Error). Because the Box-Cox transformation on which MAPE-R depends is known to be unstable, we suggest that this represents a line of further research into GMAPE, which, like MAPE-R, is subject neither to the shortcomings observed for MAPE nor to the instability of the Box-Cox transformation. While further lines of research are called for, nothing in our examination of MAPE-R here rules out its use. It also meets the National Research Council's major criteria as a summary measure of accuracy. It is subject to some cautions, but these are no more restrictive than those affecting other accuracy measures, many of which are widely used and have been for some years.
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