Book Reviews

The general nature of this book is well described in the following quotation from the author’s preface: “… I have made a selection of basic material in mathematical statistics in accordance with my own preferences and prejudices, with inclinations toward trying to make a unified and systematic presentation of classical results of mathematical statistics, together with some of the more important contemporary results in a framework of modern probability theory, without going into too many ramifications.” An early version of some of the material was issued under the same title in 1943 in lithoprinted form by the Princeton University Press. The book is intended for readers with good undergraduate backgrounds in mathematics. It starts out with a brief account of the foundations of modern probability theory, followed by chapters on distribution functions, mean values and moments, sequences of random variables, characteristic and generating functions, and special distributions. The statistical part begins with sampling theory and asymptotic sampling theory, followed by three chapters on statistical estimation (linear, nonparametric, and parametric) and two on hypothesis testing (parametric and nonparametric). The final chapters deal with sequential analysis, statistical decision functions, time series, and multivariate statistical theory. There are over 400 problems most of which are very helpful to the student and a good bibliography of 19 pages (which serves also as an author index).