Introduction to Mathematical Statistics
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H erausgegeben von
S. S. Chern 1. L. Doob 1. Douglas, jr. A. Grothendieck E. Heinz F. Hirzebruch E. Hopf W. Maak S. Mac Lane W. Magnus M. M. Postnikov F. K. Schmidt D. S. Scott K. Stein Geschiiftsfuhrende H erausgeber
B. Eckmann J. K. Moser B. L. van der Waerden
Leopold Schmetterer
Introduction to Mathematical Statistics
Translated from the German by Kenneth Wickwire
Springer-Verlag Berlin Heidelberg New York 1974
Leopold Schmetterer Professor of Statistics and Mathematics at the University of Vienna
Translator:
Kenneth Wickwire Department of Mathematics, University of Manchester
Title of the German Original Edition: Einfiihrung in die mathematische Statistik, 2. verbesserte und wesentlich erweiterte Auflage Springer-Verlag Wien New York 1966
With 11 figures
AMS Subject Classification (1970): 62-01, 62 Axx, 62 Bxx, 62 Cxx, 62D03, 62 Exx, 62 Fxx, 62 Gxx, 62 Hxx
ISBN-13: 978-3-642-65544-9 e-ISBN-13: 978-3-642-65542-5 DOl: 10.1007/978-3-642-65542-5
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 the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin· Heidelberg 1974. Library of Congress Catalog Card Number 73-15290. Softcover reprint of the hardcover 1st edition 1974 Bookbinding: Konrad Triltsch, Wiirzburg.
Preface
I have used the opportunity of the second edition of the German version being translated into English to alter and improve some details. Of course I tried to correct misprints and errata of the original version. Moreover some proofs have been slightly changed and I hope thereby improved. In many instances more recent results have been inserted in the text, for example th~ treatment of the infinite dimensional linear programms in the third chapter and the investigation of superefficiency in the 5 th Chapter. On the whole I enlarged the references by pointing to more recent papers. In doing so I have considered the literature up to 1971. The 7th chapter is left unchanged although there has been particular progress in developing the theory of non-parametric statistical inference: Analysis and Probability theory as treated in the Introduction and in the first chapter would have been an insufficient background for this study. At least the concept of the contiguity of measures would have had to be introduced. Moreover the excellent book by 1. Hajek and 1. Sidak, "Theory of Rank Tests" has in the meantime been published. I am greatly indebted to Mr. Wickwire who translated almost the entire original text into English.-Mr. Wickwire has succeeded in rendering an almost literal translation of often linguistically difficult German structures. Let me then heartly thank my colleague Professor Pfanzagl, Un
