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408BOOK REVIEWS models, but not for exponential family models which are of wider applicability. It is not beyond the wit of man to find the exact distributions for such models. One suspects that the methods developed in the book may not be entirely adequate to distinguish between the distributions of local and global likelihood maxima. There is a discussion of the adequacy of models to deviations in formulation, but this is restricted to cases where alternative models belong to the same family (e.g. the family of curved exponential models). It would be far more interesting to consider the case of freely defined distinct models for data generation and estimation, not necessarily belonging to the same family. This practical problem, which often occurs in econometric and non-linear modelling, will remain even if the exact distribution of the maximum likelihood estimator is available for a particular model used for estimation. The authors themselves admit in their preface that the book should be considered as a progress report rather than an exposition of a complete theory, and we may presume that many of the techniques described will soon be overtaken by developments.Nevertheless the book is comprehensive, well argued and recommendable to anyone with a lively interest in the development of statistical inference.

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