EAN: 9784431552383

CONTRIBUTIONS ON THEORY OF MATHEMATICAL STATIST...

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.

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