Probability Theory and Mathematical Statistics Proceedings of the Fo
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Probability Theory and Mathematical Statistics Proceedings of the Fourth USSR - Japan Symposium, held at Tbilisi, USSR, August 23-29, 1982
Edited by K. It6 and
J.v. Prokhorov
Springer-Verlag Berlin Heidelberg New York Tokyo 1983
Editors
Jurii V. Prokhorov Steklov Mathematical Institute of the Academy of Sciences of the USSR Vavilov str, 42. Moscow 117966, USSR Kiyosi ItO Department of Mathematics. Gakushuin University 1-5-1 Mejiro, Toshima- ku. Tokyo, Japan
AMS Subject Classifications (1980): 60-XX. 62-XX ISBN 3-540-12718-6 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-12718-6 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks, Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to 'Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1983 Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr, 2146/3140-543210
PREFACE The Fourth USSR-Japan Symposium on Probability Theory and Mathematical Statistics was held at Tbilisi, Soviet Union, August 23-29, 1982.
Forty fi ve
probabilists from Japan and about 300 from the Soviet Union attended the symposium. This volume contains the papers presented by Japanese and Soviet participants to the Organizing Committee.
Records of the meetings and lists of the organizing
committee are attached at the end of the volume.
In this symposium, many young
probabilists participated and vigorous informal discussions took place. The fourth symposium,as well as the previous three ones)was very fruitful and important for mathematicians of our countries and we hope it will give rise to many interesting investigations in future. The Fourth Symposium was organized by Steklov Mathemat ical Institute (Moscow), Sector of Mathematical Statistics of the Institute of Economics and Law (Tbilisi) and Tbilisi State University with support of the Academy of Sciences of USSR and the Academy of Sciences of Georgian SSR.
It is a great pleasure for us to
express our gratitude to the Local Organizing Committee (headed by Professor G.M. Mania) and all those who have contributed to the success of the symposium and to the preparation of this volume.
Yu.V. Prokhorov
K. Ito
CONTENTS
A.N. KOLMOGOROV,
On logical foundations of probability theory ...........•....
1
M. AKAHlRA, Asymptotic deficiencies of estimators for pooled samples from the same distribution......................................................
6
V.G. ALEKSEEV, On the use of alternating kernels in nonparametric statistical estimation. . . . . . . • . • . . . • . . . • . . . . . • • • . . . • . . . . . . . . . . . . • . . . . • . • . . . . . . . • . • . • .. 15 S. AMARI,
Differential geometry of statistical inference ...........•.••.•.•.. 26
S.N. A
