Author Description

MATHEMATICAL STATISTICS By S. S. WILKS PRINCETON UNIVERSITY PRESS Princeton, New Jersey 1947 Copyright, 1943, by PRINCETON UNIVERSITY PRESS PREFACE Moat of the mathematical theory of statistics In Its present state has been developed during the past twenty years. Because of the variety of scientific fields In which statistical problems have arisen, the original contributions to this branch of applied mathematics are widely scattered In scientific literature. Most of the theory still exists only In original form. During the past few years the author has conducted a two-semester course at Princeton University for advanced undergraduates and beginning graduate students in which an attempt has been made to give the students an Introduction to the more recent develop ments in the mathematical theory of statistics. The subject matter for this course has been gleaned, for the most part, from periodical literature. Since it is impossible to cover in detail any large portion of this literature in two semesters, the course has been held primarily to the basic mathematics of the material, with just enough problems and examples for illustrative and examination purposes. Except for Chapter XI, the contents or the present set of notes constitute the basic subject matter which this course was designed to cover. Some of the material in the authors Statistical Inference 1937 has been revised and Included. In writing up the notes an attempt has been made to be as brief and concise as possible and to keep to the mathematics with a minimum of excursions into applied mathematical statistics problems. An important topic which has been omitted is that of characteristic functions of random variables, which, when used in Fourier Inversions, provide a direct and powerful method of determining certain sampling distributions and other random variable distribu tions. However, moment generating functions are used they are more easily understood by students at this level and are almost as useful