Results 11  20
of
66
Nonparametric Estimating Equations Based on a Penalized Information Criterion
, 2000
"... It has recently been observed that, given the meanvariance relation, one can improve on the accuracy of the quasilikelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for larg ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
It has recently been observed that, given the meanvariance relation, one can improve on the accuracy of the quasilikelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for large samples does the improvement become evident. The author proposes a nonparametric estimating equation that does not depend on the estimation such moments, but instead on the penalized minimization of asymptotic variance. His method provides a strong improvement over the quasilikelihood estimator and the adaptive estimators, for a wide range of sample sizes. R ESUM E Il a eteobserverecemment que pour une relation moyennevariance donnee, il est possible d'ameliorer la precision d'un estimateur de quasivraisemblance au moyen d'un estimateur adaptatif dependant des moments superieurs. L'estimation de tels moments etant toutefois instable, le gain d'e#cacite n'est appreciable que dans de ...
Exponential dispersion models and the GaussNewton algorithm
 Austral. J. Statist
, 1991
"... It is well known that the Fisher scoring iteration for generalized linear models has the same form as the GaussNewton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponent ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
It is well known that the Fisher scoring iteration for generalized linear models has the same form as the GaussNewton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the analogy with normal regression is maintained. The multinomial distribution is used as an example.
On the properties of GEE estimators in the presence of invariant covariates
 Biometrical J
, 1996
"... In this paper it is shown that the use of nonsingular block invariant matrices of covariates leads to `generalized estimating equations' estimators (GEE estimators; Liang, K.Y. & Zeger, S. (1986). Biometrika, 73(1), 1322) which are identical regardless of the `working' correlation ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
In this paper it is shown that the use of nonsingular block invariant matrices of covariates leads to `generalized estimating equations' estimators (GEE estimators; Liang, K.Y. & Zeger, S. (1986). Biometrika, 73(1), 1322) which are identical regardless of the `working' correlation matrix used. Moreover, they are efficient (McCullagh, P. (1983). The Annals of Statistics, 11(1), 5967). If on the other hand only time invariant covariates are used the efficiency gain in choosing the `correct' vs. an `incorrect' correlation structure is shown to be negligible. The results of a simple simulation study suggest that although different GEE estimators are no more identical and are no more as efficient as an ML estimator, the differences are still negligible if both time and block invariant covariates are present. Key words: Generalized estimating equations; Invariant covariates; Asymptotic properties. 1 Introduction The `generalized estimating equations' approach (GEE approach) proposed...
Local mixture models of exponential families
, 2007
"... Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpreta ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpretable way is through mixing. This paper develops and applies the idea of local mixture modelling to exponential families. It shows that the highly interpretable and flexible models which result have enough structure to retain the attractive inferential properties of exponential families. In particular, results on identification, parameter orthogonality and logconcavity of the likelihood are proved.
SAS/STAT ® 9.2 User’s Guide The GENMOD Procedure (Book Excerpt)
, 2008
"... For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is ..."
Abstract
 Add to MetaCart
For a Web download or ebook: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.22719, Commercial Computer SoftwareRestricted Rights (June 1987).
May 1990ON LIKELIHOOD RATIO TESTS OF ONESIDED HYPOTHESES IN GENERALIZED LINEAR MODELS WITH CANONICAL LINKS
"... For generalized linear models with multivariate response and natural link functions, likelihood ratio test of onesided hypothesis on the regression parameter is considered under rather general conditions. The nullasymptotic distribution of the test statistic turns out to be chibar squared. The ex ..."
Abstract
 Add to MetaCart
For generalized linear models with multivariate response and natural link functions, likelihood ratio test of onesided hypothesis on the regression parameter is considered under rather general conditions. The nullasymptotic distribution of the test statistic turns out to be chibar squared. The extension of the above results to include quasilikellihood ratio test to incorporate overdispersion when the response is univariate is also discussed. A simple example illustrates the application of the main result. Keywords and phrases: asymptotic distribution; chibar squared distribution; logistic regression; quasilikelihood;
THE ANALYSIS OF BINARY DATA WITH LARGE, UNBALANCED, AND INCOMPLETE CLUSTERS USING RATIO MEAN AND WEIGHTED REGRESSION METHODS
, 1993
"... ..."
(Show Context)
Data Analysis
, 2002
"... In this paper we introduce robust techniques for inference and model selection in the analysis of longitudinal data. Robust versions of quasilikelihood functions are obtained by building upon a set of robust estimating equations where robustness is achieved by weighting the classical estimating equ ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper we introduce robust techniques for inference and model selection in the analysis of longitudinal data. Robust versions of quasilikelihood functions are obtained by building upon a set of robust estimating equations where robustness is achieved by weighting the classical estimating equations. The robust quasilikelihood functions are then used to construct a class of test statistics for model selection. We derive the asymptotic distribution of this class of test statistics, and show its robustness properties in terms of stability of the asymptotic level and power under contamination. We also address the problem of the robust estimation of the nuisance parameters. The application to a real dataset confirms the benefit of our robust analysis. KEY WORDS: estimating equations; model selection; nuisance parameters estimation; quasilikelihoods functions; robust estimation; robust inference.