Comptes Rendus de l Académie des Sciences - Series I - Mathematics
On propose un test de rang base sur une statistique de rangs conditionnellement libre sous l'... more On propose un test de rang base sur une statistique de rangs conditionnellement libre sous l'hypothese nulle
Journal of Statistical Planning and Inference, 2008
ABSTRACT We develop statistical inferential tools for estimating and comparing conditional tail e... more ABSTRACT We develop statistical inferential tools for estimating and comparing conditional tail expecta-tion (CTE) functions, which are of considerable interest in actuarial science. In particular, we construct estimators for the CTE functions, develop the necessary asymptotic theory for the estimators, and then use the theory for constructing confidence intervals and bands for the functions. Both parametric and non-parametric approaches are explored. Simulation studies illustrate the performance of estimators in various situations. Results are obtained under min-imal assumptions, and the general Vervaat process plays a crucial role in achieving these goals.
Communications on Pure and Applied Mathematics, 1965
This work represents results obtained under Sloan Foundation grant for statistics and under U.S. ... more This work represents results obtained under Sloan Foundation grant for statistics and under U.S. Navy Contract Nonr-285(38). Reproduction in whole or in part is permitted for any purpose of the United States Government.
... 454 MADAN L. PURI AND DAN RALESCU The problem of finding estimators which are better than the... more ... 454 MADAN L. PURI AND DAN RALESCU The problem of finding estimators which are better than the best invariant estimator So(X) = X received considerable interest after the work of Stein (1956) and James & Stein (1961). ... Page 10. 462 MADAN L. PURI AND DAN RALESCU ...
Linear models in which the unobserved error constitutes a realization of some stationary ARMA pro... more Linear models in which the unobserved error constitutes a realization of some stationary ARMA process or, equivalently, ARMA processes with a linear regression trend, are considered under unspecified innovation densities. Due to serial dependence among the observations, the classical rank-based techniques, which have been developed for linear models with independent observations and unspecified error densities, do not apply; nor do
Proceedings of the National Academy of Sciences, 1988
The problem of testing a given autoregressive moving average (ARMA) model (in which the density o... more The problem of testing a given autoregressive moving average (ARMA) model (in which the density of the generating white noise is unspecified) against other ARMA models is considered. A distribution-free asymptotically most powerful test, based on a generalized linear serial rank statistic, is provided against contiguous ARMA alternatives with specified coefficients. In the case in which the ARMA model in the alternative has unspecified coefficients, the asymptotic suffi- ciency (in the sense of Hajek) of a finite-dimensional vector of rank statistics is established. This asymptotic sufficiency is used to derive an asymptotically maximin most powerful test, based on a generalized quadratic serial rank statistic. The as- ymptotically maximin optimal test statistic can be interpreted as a rank-based, weighted version of the classical Box-Pierce portmanteau statistic, to which it reduces, in some particular problems, under gaussian assumptions. Section 1. Rank Tests for Time Series Analysis
In the special case where all jumps are either parallel to the boundary or normal to it, the theo... more In the special case where all jumps are either parallel to the boundary or normal to it, the theorem is a simple consequence of Donsker and Varadhan's work on the large deviations of local time. In general, the lower estimate (for open sets) is easy to prove since the optimal change of measure is not hard to guess. Surprisingly, it is the upper estimate that requires a bit of work, mainly in obtaining explicit expressions for some associated exponential transforms (moment generating functions). A minimax theorem then shows the equivalence of the upper and lower bounds.
The shorting of an operator, hitherto considered by Krein [11] and by Anderson and Trapp [3] only... more The shorting of an operator, hitherto considered by Krein [11] and by Anderson and Trapp [3] only for positive operators, is extended to rectangular matrices and square matrices not necessarily hermitian nonnegative definite. Some applications of the shorted matrix in mathematical ...
Journal of the American Statistical Association, 1968
ABSTRACT Nonparametric methods of constructing confidence regions for the location vectors in the... more ABSTRACT Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results of Dunn [3, 4] and SIdák [15]. Certain optimality properties of the proposed methods are also established.
An asymptotic distribution theory is developed for a general class of signed-rank serial statisti... more An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models.
Comptes Rendus de l Académie des Sciences - Series I - Mathematics
On propose un test de rang base sur une statistique de rangs conditionnellement libre sous l'... more On propose un test de rang base sur une statistique de rangs conditionnellement libre sous l'hypothese nulle
Journal of Statistical Planning and Inference, 2008
ABSTRACT We develop statistical inferential tools for estimating and comparing conditional tail e... more ABSTRACT We develop statistical inferential tools for estimating and comparing conditional tail expecta-tion (CTE) functions, which are of considerable interest in actuarial science. In particular, we construct estimators for the CTE functions, develop the necessary asymptotic theory for the estimators, and then use the theory for constructing confidence intervals and bands for the functions. Both parametric and non-parametric approaches are explored. Simulation studies illustrate the performance of estimators in various situations. Results are obtained under min-imal assumptions, and the general Vervaat process plays a crucial role in achieving these goals.
Communications on Pure and Applied Mathematics, 1965
This work represents results obtained under Sloan Foundation grant for statistics and under U.S. ... more This work represents results obtained under Sloan Foundation grant for statistics and under U.S. Navy Contract Nonr-285(38). Reproduction in whole or in part is permitted for any purpose of the United States Government.
... 454 MADAN L. PURI AND DAN RALESCU The problem of finding estimators which are better than the... more ... 454 MADAN L. PURI AND DAN RALESCU The problem of finding estimators which are better than the best invariant estimator So(X) = X received considerable interest after the work of Stein (1956) and James & Stein (1961). ... Page 10. 462 MADAN L. PURI AND DAN RALESCU ...
Linear models in which the unobserved error constitutes a realization of some stationary ARMA pro... more Linear models in which the unobserved error constitutes a realization of some stationary ARMA process or, equivalently, ARMA processes with a linear regression trend, are considered under unspecified innovation densities. Due to serial dependence among the observations, the classical rank-based techniques, which have been developed for linear models with independent observations and unspecified error densities, do not apply; nor do
Proceedings of the National Academy of Sciences, 1988
The problem of testing a given autoregressive moving average (ARMA) model (in which the density o... more The problem of testing a given autoregressive moving average (ARMA) model (in which the density of the generating white noise is unspecified) against other ARMA models is considered. A distribution-free asymptotically most powerful test, based on a generalized linear serial rank statistic, is provided against contiguous ARMA alternatives with specified coefficients. In the case in which the ARMA model in the alternative has unspecified coefficients, the asymptotic suffi- ciency (in the sense of Hajek) of a finite-dimensional vector of rank statistics is established. This asymptotic sufficiency is used to derive an asymptotically maximin most powerful test, based on a generalized quadratic serial rank statistic. The as- ymptotically maximin optimal test statistic can be interpreted as a rank-based, weighted version of the classical Box-Pierce portmanteau statistic, to which it reduces, in some particular problems, under gaussian assumptions. Section 1. Rank Tests for Time Series Analysis
In the special case where all jumps are either parallel to the boundary or normal to it, the theo... more In the special case where all jumps are either parallel to the boundary or normal to it, the theorem is a simple consequence of Donsker and Varadhan's work on the large deviations of local time. In general, the lower estimate (for open sets) is easy to prove since the optimal change of measure is not hard to guess. Surprisingly, it is the upper estimate that requires a bit of work, mainly in obtaining explicit expressions for some associated exponential transforms (moment generating functions). A minimax theorem then shows the equivalence of the upper and lower bounds.
The shorting of an operator, hitherto considered by Krein [11] and by Anderson and Trapp [3] only... more The shorting of an operator, hitherto considered by Krein [11] and by Anderson and Trapp [3] only for positive operators, is extended to rectangular matrices and square matrices not necessarily hermitian nonnegative definite. Some applications of the shorted matrix in mathematical ...
Journal of the American Statistical Association, 1968
ABSTRACT Nonparametric methods of constructing confidence regions for the location vectors in the... more ABSTRACT Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results of Dunn [3, 4] and SIdák [15]. Certain optimality properties of the proposed methods are also established.
An asymptotic distribution theory is developed for a general class of signed-rank serial statisti... more An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models.
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