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Introduction to Mathematical Statistics_6th edition_Hogg McKean ....pdf

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    Book Cover
    Title Page
    CONTENTS
    Preface
    1. Probability and Distributions
    2. Multivariate Distributions
    3. Some Special Distributions
    4. Unbiasedness, Consistency, and Limiting Distributions
    5. Some Elementary Statistical Inferences
    6. Maximum Likelihood Methods
    7. Sufficiency
    8. Optimal Tests of Hypotheses
    9. Inferences about Normal Models
    10. Nonparametric Statistics
    11. Bayesian Statistics
    12. Linear Models
    App. A: Mathematics
    App. B: R and S-PLUS Functions
    App. C: Tables of Distributions
    App. D: References
    App. E: Answers to Selected Exercises
    INDEX
    INTERNATIONAL EDITION Introduction to MathelYlatical Statistics Sixth Edition Hogg · McKean · Craig
    Introduction to Mathematical Statistics Sixth Edition Robert V. Hogg University of Iowa Joseph W. McKean Western Michigan University Allen T. Craig Late Professor of Statistics University of Iowa Pearson Education International
    If you purchased this book within the United States or Canada, you should be aware that it has been wrongly imported without the approval of the Publisher or Author. Executive Acquisitions Editor: George Lobell Executive Editor-in-Chief: Sally Yagan Vice President/Director of Production and Manufacturing: David W. Riccardi Production Editor: Bayani Mendoza de Leon Senior Managing Editor: Linda Mihatov Behrens Executive Managing Editor: Kathleen Schiaparelli Assistant Manufacturing Manager/Buyer: Michael Bell Manufacturing Manager: Trudy Pis ciotti Marketing Manager: Halee Dinsey Marketing Assistant: Rachael Beckman Art Director: Jayne Conte Cover Designer: Bruce Kenselaar Art Editor: Thomas Benfatti Editorial Assistant: Jennifer Brody Cover Image: Tun shell (Tonna galea). David Roberts/Science Photo Librory/Photo Researchers, Inc. ©2005, 1995, 1978, 1970, 1965, 1958 Pearson Education, Inc. Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ 07458 All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Pearson Prentice Hall® is a trademark of Pearson Education, Inc. Printed in the United States of America 109876543 ISBN: 0-13-122605-3 Pearson Education, Ltd., London Pearson Education Australia PTY. Limited, Sydney Pearson Education Singapore, Pte., Ltd Pearson Education North Asia Ltd, Hong Kong Pearson Education Canada, Ltd., Toronto Pearson Education de Mexico, S.A. de C.V. Pearson Education - Japan, Tokyo Pearson Education Malaysia, Pte. Ltd Pearson Education, Upper Saddle River, New Jersey
    To Ann and to Marge
    Contents Preface 1 Probability and Distributions 1.1 Introduction . . . . . . . . . . 1.2 Set Theory . . . . . . . . . . 1.3 The Probability Set Function 1.4 Conditional Probability and Independence. 1.5 Random Variables 1.6 Discrete Random Variables .. 1.6.1 Transformations .... 1. 7 Continuous Random Variables. 1. 7.1 Transformations .... . . . . . 1.8 Expectation of a Random Variable 1.9 Some Special Expectations 1.10 Important Inequalities . . . . . . . 2 Multivariate Distributions 2.1 Distributions of Two Random Variables 2.1.1 Expectation . . . . . . . . . . . . 2.2 Transformations: Bivariate Random Variables. 2.3 Conditional Distributions and Expectations 2.4 The Correlation Coefficient 2.5 2.6 Extension to Several Random Variables . . . . . . . Independent Random Variables . . . . . 2.6.1 • Variance-Covariance ... 2.7 Transformations: Random Vectors 3 Some Special Distributions 3.1 The Binomial and Related Distributions 3.2 The Poisson Distribution ... 3.3 The r, X2 , and {3 Distributions 3.4 The Normal Distribution .... 3.4.1 Contaminated Normals 3.5 The Multivariate Normal Distribution v xi 1 1 3 11 22 33 41 43 45 47 53 59 68 73 73 79 84 93 101 108 115 121 124 133 133 143 149 160 167 171
    vi Contents 3.6 * Applications ... 3.5.1 t and F-Distributions " 3.6.1 The t-distribution 3.6.2 The F-distribution 3.6.3 Student's Theorem 3.7 Mixture Distributions " 4 U nbiasedness, Consistency, and Limiting Distributions 4.1 Expectations of Functions . . 4.2 Convergence in Probability .. 4.3 Convergence in Distribution . . 4.3.1 Bounded in Probability 4.3.2 ~-Method . . . . . . . . 4.3.3 Moment Generating Function Technique . 4.4 Central Limit Theorem . . . . . . . . . . . * Asymptotics for Multivariate Distributions 4.5 5 Some Elementary Statistical Inferences 5.1 Sampling and Statistics 5.2 Order Statistics . . . . . . . . . . . . . . 5.2.1 Quantiles . . . . . . . . . . . . . 5.2.2 Confidence Intervals of Quantiles 5.3 *Tolerance Limits for Distributions . . . 5.4 More on Confidence Intervals . . . . . . 5.4.1 Confidence Intervals for Differences in Means 5.4.2 Confidence Interval for Difference in Proportions Introduction to Hypothesis Testing . . . . . . 5.5 5.6 Additional Comments About Statistical Tests 5.7 Chi-Square Tests . . . . . . . . . . . . . . . . 5.8 The Method of Monte Carlo . . . . . . . . . . 5.8.1 Accept-Reject Generation Algorithm. 5.9 Bootstrap Procedures . . . . . . . . . . . . . 5.9.1 Percentile Bootstrap Confidence Intervals 5.9.2 Bootstrap Testing Procedures . 6 Maximum Likelihood Methods 6.1 Maximum Likelihood Estimation . . . . . 6.2 Rao-Cramer Lower Bound and Efficiency 6.3 Ma.ximum Likelihood Tests .... 6.4 Multiparameter Case: Estimation. 6.5 Multiparameter Case: Testing. 6.6 The EM Algorithm . . . . . . . . . 177 182 182 184 186 189 197 198 203 207 213 214 216 220 226 233 233 238 242 245 250 254 257 260 263 272 278 286 292 297 297 301 311 311 319 333 342 351 359
    Contents 7 Sufficiency 7.1 Measures of Quality of Estimators 7.2 A Sufficient Statistic for a Parameter. 7.3 Properties of a Sufficient Statistic. . . 7.4 Completeness and Uniqueness . . . . . 7.5 The Exponential Class of Distributions. 7.6 Functions of a Parameter . . . . . . . . 7.7 The Case of Several Parameters . . . . . 7.8 Minimal Sufficiency and Ancillary Statistics 7.9 Sufficiency, Completeness and Independence. 8 Optimal Tests of Hypotheses 8.1 Most Powerful Tests . . . . 8.2 Uniformly Most Powerful Tests 8.3 Likelihood Ratio Tests . . . . . 8.4 The Sequential Probability Ratio Test 8.5 Minimax and Classification Procedures . 8.5.1 Minimax Procedures 8.5.2 Classification....... 9 Inferences about Normal Models 9.1 Quadratic Forms . . . . . . . . . 9.2 One-way ANOVA . . . . . . . . . 9.3 Noncentral X2 and F Distributions 9.4 Multiple Comparisons . . 9.5 The Analysis of Variance 9.6 A Regression Problem . . 9.7 A Test of Independence . 9.8 The Distributions of Certain Quadratic Forms. 9.9 The Independence of Certain Quadratic Forms vii 367 367 373 380 385 389 394 398 406 411 419 419 429 437 448 455 456 458 463 463 468 475 477 482 488 498 501 508 10 Nonparametric Statistics 10.1 Location Models . . . . . . . . . . . . 10.2 Sample Median and Sign Test . . . . . 10.2.1 Asymptotic Relative Efficiency 10.2.2 Estimating Equations Based on Sign Test 10.2.3 Confidence Interval for the Median. 515 515 518 523 528 529 531 536 539 539 541 10.4.1 Asymptotic Relative Efficiency 545 10.4.2 Estimating Equations Based on the Mann-Whitney-Wilcoxon 547 10.4.3 Confidence Interval for the Shift Parameter I:l. . 547 10.5 General Rank Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Signed-Rank Wilcoxon. . . . . . . . . . . . . . . 10.3.1 Asymptotic Relative Efficiency . . . . . . 10.3.2 Estimating Equations Based on Signed-rank Wilcoxon 10.3.3 Confidence Interval for the Median . 10.4 Mann-Whitney-Wilcoxon Procedure
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