Quasi-Likelihood And Its Application: A General Approach to Optimal Parameter Estimation (Springer Series in Statistics) - Hardcover

Heyde, Christopher C.

Hardcover

ISBN 10: 0387982256 ISBN 13: 9780387982250

Publisher: Springer, 1997

Synopsis

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.

About this title

About the Author

Christopher Heyde is Professor of Statistics at both Columbia University in New York and the Australian National University in Canberra. He is also Director of the Center for Applied Probability at Columbia. He is a Fellow of the Australian Academy of Science and has been Foundation Dean of the School of Mathematical Sciences at the Australian National University and Foundation Director of the Key Centre for Statistical Sciences in Melbourne. He has served as President of the Bernoulli Society and Vice President of the International Statistical Institute and is Editor-in-Chief of the international probability journals "Journal of Applied Probability" and "Advances in Applied Probability". He has done considerable distinguished research in probability and statistics which has been honoured by the awards of the Pitman Medal (1988) and Hannan Medal.

From the Inside Flap

"The powerful message of this timely book is that 'for estimation of parameters in stochastic systems of any kind . . . it is possible to replace likelihood-based techniques by quasi-likelihood alternatives, in which only assumptions about means and variances are made in order to obtain estimators. There is often little, if any, loss in efficiency . . . ' Chris Heyde has played a major role in the development of QLE. Much of the work in this wonderful book can be traced directly or indirectly to his ideas. We are fortunate that he has added his insight to this authoritative work, which describes a field that has matured to the point that it is now ready to fulfill its promise of becoming a standard tool of statistical analysis." --Journal of the American Statistical Association

"When reading this book we really understand how deep and effective this approach is when solving diverse inference problems in a very satisfactory way . . . In a master style the author demonstrates by example how a particular property can be developed into a general result." --Journal of Applied Mathematics and Stochastic Analysis

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0387982256
• ISBN 13: 9780387982250
• Binding: Hardcover
• Number of pages: 246