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202 Reviews [Part 2, special schemes, in a clear and concise manner, with plenty of worked examples. It also considers continuous sampling plans and cumulative results plans (i.e. skip-lot and chain sampling) to a much more detailed level than that usually found in textbooks. The final chapter on administration of acceptance sampling is particularly useful, since here it details how one should decide upon a particular scheme, comparing the properties of the various schemes available, and an outline as to how to derive values for the parameters, such as AQL, IQL, etc., to be specified. This is a topic usually given only a cursory mention in other books. The book does not go into the deeper statistical theory behind the sampling plans at any point, and the angle is always the classical approach, ignoring the economic approach completely. Should anyone want to go further into a topic, numerous references are given. The book serves admirably the market for which it was designed - those implementing quality control on the factory floor and for this purpose it is one of the best books to be released for several years. J. Curram University of Kent 15. Non-negative Matrices and Markov Chains. By E. Seneta. New York, Springer-Verlag, 1981. xiii, 279 p. 22 cm. Unpriced. This is the second edition of the earlier book by Seneta which had the shorter title "Non negative matrices" and which was published by George Allen and Unwin in 1973. One reason for the new title is said to be the clarification of the probabilistic nature of the original book while another is the emphasis of the increased Markov chain content in this new edition. Substantial additions and modifications have been made throughout the text. The most notable are as follows. A new Chapter 3 discusses inhomogeneous products of non-negative matrices and replaces a shorter section in the first edition, while Chapter 4, on Markov chains and finite stochastic matrices, has been extensively revised with new material incorporated. Finally a new chapter on truncations of infinite stochastic matrices discusses the calculation of the invariant distribution of a Markov chain with a countably infinite number of states using a succession of finite truncations of the transition matrix. The original list of references has been updated only in so far as it includes references cited in new portions of the text. The author Goes, however, point out the existence of a more recent (1979) bibliography. Those unfamiliar with the first edition may like to know that useful bibliographic notes and discussion are given at the end of each section of the book, together with a substantial set of exercises, many of which extend or elaborate results in the text. Some twenty pages of appendices summarize background material on (a) elementary number theory, (b) general matrix lemmas and (c) upper semicontinuous functions. The book is well-written and, in the new edition, very clearly laid out and printed. It provides a most useful compilation of, and reference for, non-negative matrix results particularly in the field of Markov chains, although there are important applications in other areas, such as demo graphy and mathematical economics. Valerie Isham University College London 16. Prior Information in the Linear Model. By H. Toutenberg. Chichester and New York, Wiley, 1982.215 p. 24 em, £16.50. I think one might be forgiven for believing from its title that this book dealt at least in part with Bayesian inference and the linear model. In fact it is completely classical in its orientation. It contains sections on the General Linear Model, Mixed Estimation, Minimax Estimation, Prob lems of Model Choice and Prior Information in Econometric Models. The author's stated aim is to handle in depth some topics in Classical inference claimed as so far poorly documented e.g. robustness of minimax estimators, restricted least squares, two stage least squares estimators and mixed estimators where part of the information is allowed to be incorrect. Th~ book is written in a clear if rather mathematical style. There are very few numerical examples of the different estimators. Furthermore, I could find no examples of practical prob lems which were transformed into the types of mathematical structures considered so that the consequent inference was given a concrete context. This was even the case in the last section on
Journal of the Royal Statistical Society Series A (Statistics in Society) – Oxford University Press
Published: Dec 5, 2018
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