 Presents systematically the author’s contributions to various problems of mathematical statistics
 Provides an English translation by the author of some known results originally published in Japanese
 Deals in a systematic and comprehensive manner with problems that hitherto were not well articulated
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 About this book

This volume is a reorganized edition of Kei Takeuchi’s works on various problems in mathematical statistics based on papers and monographs written since the 1960s on several topics in mathematical statistics and published in various journals in English and in Japanese. They are organized into seven parts, each of which is concerned with specific topics and edited to make a consistent thesis. Sometimes expository chapters have been added. The topics included are as follows: theory of statistical prediction from a nonBayesian viewpoint and analogous to the classical theory of statistical inference; theory of robust estimation, concepts, and procedures, and its implications for practical applications; theory of location and scale covariant/invariant estimations with derivation of explicit forms in various cases; theory of selection and testing of parametric models and a comprehensive approach including the derivation of the Akaike’s Information Criterion (AIC); theory of randomized designs, comparisons of random and conditional approaches, and of randomized and nonrandomized designs, with random sampling from finite populations considered as a special case of randomized designs and with some separate independent papers included. Theory of asymptotically optimal and higherorder optimal estimators are not included, since most of them already have been published in the Joint Collected Papers of M. Akahira and K. Takeuchi. There are some topics that are not necessarily new, do not seem to have attracted many theoretical statisticians, and do not appear to have been systematically dealt with in textbooks or expository monographs. One purpose of this volume is to give a comprehensive view of such problems as well.
 About the authors

Professor Emeritus, The University of Tokyo
 Table of contents (15 chapters)


Theory of Statistical Prediction
Pages 337

Unbiased Estimation in Case of the Class of Distributions of Finite Rank
Pages 4157

Some Theorems on Invariant Estimators of Location
Pages 5985

Robust Estimation and Robust Parameter
Pages 89101

Robust Estimation of Location in the Case of Measurement of Physical Quantity
Pages 103147

Table of contents (15 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Contributions on Theory of Mathematical Statistics
 Authors

 Kei Takeuchi
 Copyright
 2020
 Publisher
 Springer Japan
 Copyright Holder
 Springer Japan KK, part of Springer Nature
 eBook ISBN
 9784431552390
 DOI
 10.1007/9784431552390
 Hardcover ISBN
 9784431552383
 Edition Number
 1
 Number of Pages
 XI, 435
 Number of Illustrations
 17 b/w illustrations
 Topics