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 non-Bayesian 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 non-randomized 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 higher-order 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.
