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Parametric statistical inference. (English) Zbl 0855.62002
Oxford: Clarendon Press. xviii, 490 p. (1996).
Methods of parametric statistical inference are based on two schools of thought, one is based on the frequentist philosophy and the other on the Bayesian philosophy. Both are based on the concept of a likelihood function. The author has written a nice, readable book bringing these two concepts together at a level understandable to students, with exponential families as the building blocks for modelling. Even though he says “all models are wrong”, he does agree with the fact “in order to make a decision, one must usually assume that the model involved is correct for a decision to be possible”. The contents are as follows :
Chapter 1: Model building; Chapter 2: Exponential family of probability distributions; Chapter 3: Likelihood; Chapter 4: Goodness of fit; Chapter 5: Asymptotics; Chapter 6: Factoring the likelihood function; Chapter 7: Frequentist decision-making; Chapter 8: Bayesian decision-making; Chapter 9: Poisson regression; Chapter 10: Binomial regression. Appendices A: Elements of measure theory; B: Review of probability theory; C: Normal distribution statistics; D: Numerical methods.
The author attempted “to look at how applied statisticians actually have come to make inferences and not how mathematical statisticians think they should” and he succeded in his efforts! The results are not proved in a rigorous manner but sketched at times. The material covered is up to date. The book is useful more as a reference work rather than as a text book even though a selected material can be used for specially designed courses either at an advanced undergraduate level or at a graduate level. Each chapter has a set of exercises at the end.
I strongly recommend the book for any student or researcher of “Statistical Inference” and also to all (mathematical) statisticians.

62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62Fxx Parametric inference
62C10 Bayesian problems; characterization of Bayes procedures
62C05 General considerations in statistical decision theory