Quasi-Likelihood And Its Application

1. Front Matter

   Pages i-ix

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2. Introduction

   Pages 1-10

3. The General Framework

   Pages 11-41

4. An Alternative Approach: E-Sufficiency

   Pages 43-51

5. Asymptotic Confidence Zones of Minimum Size

   Pages 53-67

6. Asymptotic Quasi-Likelihood

   Pages 69-89

7. Combining Estimating Functions

   Pages 91-105

8. Projected Quasi-Likelihood

   Pages 107-128

9. Bypassing the Likelihood

   Pages 129-139

10. Hypothesis Testing

    Pages 141-145

11. Infinite Dimensional Problems

    Pages 147-151

12. Miscellaneous Applications

    Pages 153-177

13. Consistency and Asymptotic Normality for Estimating Functions

    Pages 179-197

14. Complements and Strategies for Application

    Pages 199-210

15. Back Matter

    Pages 211-235

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This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random e?ects 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 ?rst 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 ?nding 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.

• Estimator
• Generalized linear model
• Likelihood
• Mathematica
• STATISTICA
• Variance
• optimization
• probability
• statistics
• stochastic process

• Stochastic Analysis Program, SMS, Australian National University, Canberra, Australia

  Christopher C. Heyde

• Department of Statistics, Columbia University, New York, USA

  Christopher C. Heyde

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