因为是第二卷，因此是从第九章开始的，大家各取所需吧。
Analysis of Variance for Random Models Volume II-Unbalanced Data Theory, Methods, Applications, and Data Analysis

Hardeo Sahai
Center for Addiction Studies
School of Medicine
Universidad Central del Caribe
Bayamon, Puerto Rico 00960-6032
USA
Library of Congress Cataloging-in-Publication Data
Sahai, Hardeo.
Analysis of variance from random models : theory, methods, applications, and data analysis
/Hardeo Sahai, Mario Miguel Ojeda.
p. cm.
Includes bibliographical references and index.
Contents: v.1. Balanced data.
ISBN 0-8176-3230-1 (v. 1: alk. paper)
1. Analysis of variance. I. Ojeda, Mario Miguel, 1959- II. Title.
QA279.S23 2003
519.5
38–dc22 20030630260
ISBN 0-8176-3229-8 Volume II Printed on acid-free paper.
9 Matrix Preliminaries and General Linear Model 1
9.1 Generalized Inverse of a Matrix . . . . . . . . . . . . . . . . 3
9.2 Trace of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . 4
9.3 Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . 4
9.4 General Linear Model . . . . . . . . . . . . . . . . . . . . . 6
9.4.1 Mathematical Model . . . . . . . . . . . . . . . . 6
9.4.2 Expectation Under Fixed Effects . . . . . . . . . . 7
9.4.3 Expectation Under Mixed Effects . . . . . . . . . . 8
9.4.4 Expectation Under Random Effects . . . . . . . . . 9
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
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17.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 371
17.2 Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . 372
17.3 Expected Mean Squares . . . . . . . . . . . . . . . . . . . . 375
17.4 Estimation of Variance Components . . . . . . . . . . . . . . 376
17.4.1 Analysis of Variance Estimators . . . . . . . . . . . 376
17.4.2 Symmetric Sums Estimators . . . . . . . . . . . . 377
17.4.3 Other Estimators . . . . . . . . . . . . . . . . . . . 381
17.5 Variances of Estimators . . . . . . . . . . . . . . . . . . . . 382
17.6 Confidence Intervals and Tests of Hypotheses . . . . . . . . 382
17.7 A Numerical Example . . . . . . . . . . . . . . . . . . . . . 385
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
Appendices 391
A Two Useful Lemmas in Distribution Theory . . . . . . . . . 391
B Some Useful Lemmas for a Certain Matrix . . . . . . . . . . 393
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 393
C Incomplete Beta Function . . . . . . . . . . . . . . . . . . . 394
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 395
D Incomplete Inverted Dirichlet Function . . . . . . . . . . . . 395
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 397
E Inverted Chi-Square Distribution . . . . . . . . . . . . . . . 397
F The Satterthwaite Procedure . . . . . . . . . . . . . . . . . . 397
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 400
G Maximum Likelihood Estimation . . . . . . . . . . . . . . . 400
H Some Useful Lemmas on the Invariance Property of the
ML Estimators . . . . . . . . . . . . . . . . . . . . . . . . . 402
I Complete Sufficient Statistics and the Rao–Blackwell and
Lehmann–Sheffé Theorems . . . . . . . . . . . . . . . . . . 403
J Point Estimators and the MSE Criterion . . . . . . . . . . . . 403
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 404
K Likelihood Ratio Test . . . . . . . . . . . . . . . . . . . . . 405
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . 405