MINIMIZING AVERAGE RISK IN REGRESSION MODELS

2006

Most model selection mechanisms work in an 'overall' modus, providing models without speciffic concern for how the selected model is going to be used afterwards. The focussed information criterion (FIC), on the other hand, is geared towards optimum model selection when inference is required for a given estimand. In this paper the FIC method is extended to weighted versions. This allows one to rank and select candidate models for the purpose of handling a range of similar tasks well, as opposed to being forced to focus on each task separately. Applications include selecting regression models that perform well for speciffied regions of covariate values. We derive these wFIC criteria, give asymptotic results, and apply the method store al data. Formulae for easy implementation are provided for the class of generalised linear models.

Economic Modelling, 2012

In contrast to conventional measures, the Focused Information Criterion (FIC) allows the purpose-specifi c selection of models, thereby refl ecting the idea that one kind of model might be appropriate for inferences on a parameter of interest, but not for another. Ever since its invention, the FIC has been increasingly applied in the realm of statistics, but this concept appears to be virtually unknown in the economic literature. Using a straightforward analytical example, this paper provides for a didactic illustration of the FIC and shows its usefulness in economic applications. JEL Classifi cation: C3, D2 ; Manuel Frondel, RUB and RWI; Harald Tauchmann, RWI. -We are greatly indebted to Christoph M. Schmidt and Colin Vance for their invaluable comments and suggestions. This work has been supported in part by the Collaborative Research

Journal of The American Statistical Association, 2004

This article is concerned with variable selection methods for the proportional hazards regression model. Including too many covariates causes extra variability and inflated confidence intervals for regression parameters, so regimes for discarding the less informative ones are needed. Our framework has p covariates designated as 'protected' while variables from a further set of q covariates are examined for possible in-or exclusion. In addition to deriving results for the AIC method, defined via the partial likelihood, we develop a focussed information criterion that for given interest parameter finds the best subset of covariates. Thus the FIC might find that the best model for predicting median survival time might be different from the best model for estimating survival probabilities, and the best overall model for analysing survival for men might not be the same as the best overall model for analysing survival for women. We also develop methodology for model averaging, where the final estimate of a quantity is a weighted average of estimates computed for a range of submodels. Our methods are illustrated in simulations and for a survival study of Danish skin cancer patients.

American Journal of Theoretical and Applied Statistics, 2014

Model selection is an important part of any statistical analysis. Many tools are suggested for selecting the best model including frequentist and Bayesian perspectives. There is often a considerable uncertainty in the selection of a particular model to be the best approximating model. Model selection uncertainty arises when the data are used for both model selection and parameter estimation. Bias in estimators of model parameters often arise when data based selection has been done. Therefore, model averaging of the parameter estimators will be done to alleviate the bias in model selection in a set of candidate models, by combining the information from a set of candidate models. This paper is twofold , new criteria of model selection are proposed based on different averages of AIC, BIC, AICc, and HQC. Also, model averaging is introduced to compare the parameter estimators in model averaging with the ones in model selection. Two Simulation studies are considered, the first is for model selection and showed that the new proposed criteria are lies between some of the known criteria such as AIC, BIC, AICc, and HQC, and so they can be used as new criteria of model selection. The second simulation study is for model averaging and showed that the parameter estimators have less bias and less predicted mean square error (PMSE) compared with the parameter estimators in model selection.

The linear hazard regression model developed by Aalen is becoming an increasingly popular alternative to the Cox multiplicative hazard regression model. There are no methods in the literature for selecting among different candidate models of this nonparametric type, however. In the present chapter a focused information criterion is developed for this task. The criterion works for each specified covariate vector, by estimating the mean squared error for each candidate model’s estimate of the associated cumulative hazard rate; the finally selected model is the one with lowest estimated mean squared error. Averaged versions of the criterion are also developed.

SSRN Electronic Journal, 2011

In contrast to conventional model selection criteria, the Focused Information Criterion (FIC) allows for purpose-specifi c choice of models. This accommodates the idea that one kind of model might be highly appropriate for inferences on a particular parameter, but not for another. Ever since its development, the FIC has been increasingly applied in the realm of statistics, but this concept appears to be virtually unknown in the economic literature. Using a classical example and data for 35 U.S. industry sectors (1960-2005), this paper provides for an illustration of the FIC and a demonstration of its usefulness in empirical applications.

Journal of Physics: Conference Series, 2019

Akaike’s Information Criterion (AIC) was firstly annunced by Akaike in 1971. In linear regression modelling, AIC is proposed as a model selection criterion since it estimates the quality of each model relative to other models. In this paper we domonstrate the use of AIC criterion to estimate p, the number of selected varibles in regression linear model through a simulation study. We simulate two particular cases, namely orthogonal and non - orthogonal cases. The orthogonal case is run where there is totally no correlation between any independent variable and one dependent variable, whereas for the the orthogonal case is run where there is a correlation between some independent variables and one dependent variable. The simulation results are used to investigate of the overestimate number of independent variables selected in the model for two cases. Although the two cases produce the oversetimate number ofindependent variables, most of the time the orthogonal case still provide less o...

2004

This article is concerned with variable selection methods for the proportional hazards regression model. Including too many covariates causes extra variability and inflated confidence intervals for regression parameters, so regimes for discarding the less informative ones are needed. Our framework has p covariates designated as 'protected' while variables from a further set of q covariates are examined for possible in-or exclusion. In addition to deriving results for the AIC method, defined via the partial likelihood, we develop a focussed information criterion that for given interest parameter finds the best subset of covariates. Thus the FIC might find that the best model for predicting median survival time might be different from the best model for estimating survival probabilities, and the best overall model for analysing survival for men might not be the same as the best overall model for analysing survival for women. We also develop methodology for model averaging, where the final estimate of a quantity is a weighted average of estimates computed for a range of submodels. Our methods are illustrated in simulations and for a survival study of Danish skin cancer patients.

The Annals of Statistics, 2011

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.

Psychometrika, 2011

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n × 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a full-rank predictor correlation matrix, R xx , of order n, and for regression models with constant R 2 (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an n-dimensional ellipsoid. The population performance of alternate regression weights-such as equal weights, correlation weights, or rounded weights-can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of R 2 . To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an n-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in R n , and (3) populating the set of regression vectors that have constant cosine with a target vector in R n . Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.