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Probability with a view toward statistics. Vol. 2: Mathematical statistics. (English) Zbl 0821.62003
London: Chapman & Hall. xii, 533 p. (1994).
This is the continuation of volume 1, see the preceding review, Zbl 0821.62002. The first half of the monograph includes more advanced topics from probability while the second half contains material from mathematical statistics. The following topics are treated:
random vectors and their densities (transformation theorems, discursion and dispersion functions), stochastic processes (Gaussian processes, Poisson process, Brownian motion, Glivenko-Cantelli Theorem), regular conditional probabilities (Markov property, LIL for random walks, Tulcea’s theorem), optimal stopping strategies, exponential families, consistency of maximum estimators (including MLE) and asymptotic normality (of maximum estimators).
The character of the book is very much like that of volume 1: a deep and rigorous treatment of the theory, presented in an appealing way, combined with lots of illuminating examples, applications, remarks, references and exercises.

MSC:
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
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