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Asymptotic techniques for use in statistics. (English) Zbl 0672.62024
Monographs on Statistics and Applied Probability. London etc.: Chapman and Hall. x, 252 p. £25.00 (1989).
This is an interesting book for advanced students of statistics and probability and research workers who want to know mathematical techniques of asymptotic theory useful in statistics and applied probability. To study the asymptotic properties of distributions of statistics, we usually use one of the following three methods: (i) examining the form of the random variable in question, (ii) analyzing the density or cumulative distribution, (iii) studying the moment or cumulant generating function.
In this book, by using a number of examples, the authors explain ingeniously and systematically these methods both in the univariate case and in the multivariate one. Especially in the latter case, they use tensor methods which often enable the multivariate versions of the formulae in the univariate case to be not more complicated than the univariate and also univariate calculations to be more transparent.
The emphasis is placed on the study of asymptotic expansions for probability distributions. But, it should be noted that to apply the results some judgement is usually required.
Reviewer: K.-I.Yoshihara

62E20 Asymptotic distribution theory in statistics
62-02 Research exposition (monographs, survey articles) pertaining to statistics