Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation
This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random effects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the first order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its application to generalized linear model type contexts, while that of optimal estimating functions has embraced a broader concept. There is, however, no essential distinction between the underlying ideas and the term quasi-likelihood has herein been adopted as the general label. This emphasizes its role in extension of likelihood based theory. The idea throughout involves finding quasi-scores from families of estimating functions. Then, the qua- likelihood estimator is derived from the quasi-score by equating to zero and solving, just as the maximum likelihood estimator is derived from the like- hood score.
1113635891
Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation
This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random effects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the first order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its application to generalized linear model type contexts, while that of optimal estimating functions has embraced a broader concept. There is, however, no essential distinction between the underlying ideas and the term quasi-likelihood has herein been adopted as the general label. This emphasizes its role in extension of likelihood based theory. The idea throughout involves finding quasi-scores from families of estimating functions. Then, the qua- likelihood estimator is derived from the quasi-score by equating to zero and solving, just as the maximum likelihood estimator is derived from the like- hood score.
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Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation

Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation

by Christopher C. Heyde
Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation

Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation

by Christopher C. Heyde

Overview

This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random effects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the first order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its application to generalized linear model type contexts, while that of optimal estimating functions has embraced a broader concept. There is, however, no essential distinction between the underlying ideas and the term quasi-likelihood has herein been adopted as the general label. This emphasizes its role in extension of likelihood based theory. The idea throughout involves finding quasi-scores from families of estimating functions. Then, the qua- likelihood estimator is derived from the quasi-score by equating to zero and solving, just as the maximum likelihood estimator is derived from the like- hood score.

Product Details

ISBN-13: 9780387982250
Publisher: Springer New York
Publication date: 07/31/1997
Series: Springer Series in Statistics
Edition description: 1997
Pages: 236
Product dimensions: 6.14(w) x 9.21(h) x 0.03(d)

Table of Contents

The General Framework.- An Alternative Approach: E-Sufficiency.- Asymptotic Confidence Zones of Minimum Size.- Asymptotic Quasi-Likelihood.- Combining Estimating Functions.- Projected Quasi-Likelihood.- Bypassing the Likelihood.- Hypothesis Testing.- Infinite Dimensional Problems.- Miscellaneous Applications.- Consistency and Asymptotic Normality for Estimating Functions.- Complements and Strategies for Application.
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