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This is author-approved bcc: Quasi-likelihood is a very generally applicable estimating function based methodology for optimally estimating model parameters in systems subject to random effects. Only assumptions about means and covariances are required in contrast to the full distributional assumptions of ordinary likelihood based methodology. This monograph gives the first account in book form of all the essential features of the quasi-likelihood methodology,and stresses its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential princples rather than detailed proofs. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided. Readers are assumed to have a firm grounding in probability and statistics at the graduate level. 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),Hannan Medal
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.
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.