文档介绍：The EM Algorithm and Extensions
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,i THRIYAMBAKAM KRISHNAN
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A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
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Copyright © 1997 by John Wiley & Sons, Inc.
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Library ofCongress Cataloging in Publication Data:
McLachlan, Geoffrey J., 1946-
The EM algorithm and extensions / GJ. McLachlan and T. Krishnan.
p. em. - (Wiley series in probability and statistics.
Applied probability and statistics)
Includes bibliographical references and index.
ISBN 0-471-12358-7 (alk. paper)
I. Expectation-maximization algorithms. 2. Estimation theory.
3. Missing observations (Statistics) I. Krishnan, T.
(Thriyambakam), 1938- . II. Title. III. Series.
1996
'44-DC20 96-38417
CIP
Printed in the United States ofAmerica
10 9 8 7 6 5 4 3 2 I
To
Beryl, Jonathan, and Robbie
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Contents
Preface XIII'"
1. General Introduction 1
Introduction, I
Maximum Likelihood Estimation, 3
;
Newton-Type Methods,S
Introduction, 5
Newton-Raphson Method, 5
Quasi-Newton Methods, 6
Modified Newton Methods, 7
Introductory Examples, 9
Introduction, 9
Example : A Multinomial Example, 9
Example : Estimation ofMixing Proportions, 16
Formulation ofthe EM Algorithm, 21
EM Algorithm, 21
Example : Censored Exponentially Distributed
~
". Survival Times, 23
t'
I" E- and M-Steps for Regula