.

0 (hodnocen0 x )

BK

Amsterdam : North-Holland, 1988

xvi, 1002 s.

ISBN 0-444-85335-9

000036917

Preface vii // Contributors xvii // Ch. 1. Estimation of Variance Components 1 // C. R. Rao and J. Kleffe // 1. Introduction 1 // 2. Models of variance and covariance components 4 // 3. Estimability 8 // 4. Minimum variance unbiased estimation (normal case) 12 // 5. Minimum norm quadratic estimation (MINQE-theory) 16 // 6. Maximum likelihood estimation 32 References 37 // Ch. 2. Multivariate Analysis of Variance of Repeated Measurements 41 // N. H. Timm // 1. Introduction 41 // 2. The general linear model 41 // 3. One-sample repeated measurement design 46 // 4. The /-sample repeated measurement design 50 // 5. Factorial design structures 57 // 6. Crossover/changeover design 63 // 7. Multivariate repeated measurements 68 // 8. Growth curve analysis 74 // 9. Summary 84 References 84 // Ch. 3. Growth Curve Analysis 89 // S. Geisser // 1. Repeated measurements-the profile background 89 // 2. Growth curve models 92 // ix // x // Table of contents // 3. Classical multivariate model-frequentist analysis 93 // 4. A Bayesian approach-estimation 100 // 5. Bayesian prediction-simple structure 103 // 6. Bayesian prediction-arbitrary covariance case 105 // 7. Individual growth curves 106 // 8. A sample reuse approach for conditional prediction 110 // 9. Group growth curve comparisons 111 // 10. Concluding remarks 113 // References 114 // Ch. 4. Bayesian Inference in MANOVA 117 // S. J. Press // 1. Introduction 117 // 2. Assumptions of the model 118 // 3. Estimation 118 // 4. MANOVA models 126 References 131 // Ch. 5. Graphical Methods for Internal Comparisons in ANOVA and MANOVA 133 // R. Gnanadesikan // 1. Introduction 133 // 2. Quantile-quantile (Q-Q) probability plots 135 // 3. Specific Q-Q plots for ANOVA and MANOVA 138 // 4. Summary and conclusions 167 // Appendix I. Computations of quantiles 168 //

Appendix II. Computation of maximum likelihood estimates (mle) of parameters of a gamma distribution 173 References 176 // Ch. 6. Monotonicity and Unbiasedness Properties of ANOVA and MANOVA Tests 179 // S. Das Gupta // 1. Introduction 179 // 2. Monotonicity of the power functions of the UMP invariant tests in the two special cases 181 // 3. Mathematical preliminaries 183 // 4. Study on monotonicity in the general case 188 // 5. General MANOVA models 193 // 6. Bibliographical notes 195 // 7. Some new results 196 References 196 // x // Table of contents // 3. Classical multivariate model-frequentist analysis 93 // 4. A Bayesian approach-estimation 100 // 5. Bayesian prediction-simple structure 103 // 6. Bayesian prediction-arbitrary covariance case 105 // 7. Individual growth curves 106 // 8. A sample reuse approach for conditional prediction 110 // 9. Group growth curve comparisons 111 // 10. Concluding remarks 113 // References 114 // Ch. 4. Bayesian Inference in MANOVA 117 S. J. Press // 1. Introduction 117 // 2. Assumptions of the model 118 // 3. Estimation 118 // 4. MANOVA models 126 References 131 // Ch. 5. Graphical Methods for Internal Comparisons in ANOVA and MANOVA 133 R. Gnanadesikan // 1. Introduction 133 // 2. Quantile-quantile (Q-Q) probability plots 135 // 3. Specific Q-Q plots for ANOVA and MANOVA 138 // 4. Summary and conclusions 167 // Appendix I. Computations of quantiles 168 // Appendix II. Computation of maximum likelihood estimates (mle) of parameters of a gamma distribution 173 References 176 // Ch. 6. Monotonicity and Unbiasedness Properties of ANOVA and MANOVA Tests 179 S. Das Gupta // 1. Introduction 179 // 2. Monotonicity of the power functions of the UMP invariant tests in the two special cases 181 // 3. Mathematical preliminaries 183 // 4. Study on monotonicity in the general case 188 // 5. General MANOVA models 193 //

6. Bibliographical notes 195 // 7. Some new results 196 References 196 // Ch. 7. Robustness of ANOVA and MANOVA Test Procedures 199 // P. K. Ito // 1. Introduction 199 // 2. One-way classification, fixed-effects ANOVA and MANOVA models 200 // 3. Effects of nonnormality and/or heteroscedasticity on the ANOVA F-test 205 // 4. Effects of nonnormality and/or heteroscedasticity on MANOVA tests 220 References 234 // Ch. 8. Analysis of Variance and Problems under Time Series Models 237 // D. R. Brillinger // 1. Introductory remarks 237 // 2. Growth curves 239 // 3. Field experiments 240 // 4. Responses that are covariance stationary time series 242 // 5. Further considerations 266 Acknowledgements 272 Appendix 272 References 273 Additional references 278 // Ch. 9. Tests of Unvariate and Multivariate Normality 279 // K. V. Mardia // 1. Introduction 279 // 2. Tests based on descriptive measures 280 // 3. Shapiro-Wilk’s W-test and its modifications 286 // 4. Likelihood approach 290 // 5. Goodness-of-fit tests 293 // 6. Miscellaneous tests 298 // 7. Power studies 304 // 8. Tests of multivariate normality 310 Acknowledgement 317 References 317 // Ch. 10. Transformations to Normality 321 // G. Kaskey, B. Kolman, P. R. Krishnaiah and L. Steinberg // 1. Introduction 321 // 2. Pearson type curves 322 // 3. Transformation of Pearson-type distributions 327 // 4. Evaluation of initial conditions 330 // Table of contents // 5. Integration of transformation equation 335 // 6. Statistical analysis of transistor data 337 References 340 // Ch. 11. ANOVA and MANOVA: Models for Categorical Data 343 V. P. Bhapkar // 1. Introduction and notation 343 // 2. Log-linear representation 346 // 3. Methods of estimation 349 // 4. Tests of goodness of fit of models 355 // 5. Tests for nested models 359 // 6. Some models for one population 362 // 7. ANOVA models for several populations 368 //

8. MANOVA models for several populations 375 // 9. Computation 381 // 10. Exact tests 382 // 11. Conditional tests 383 // 12. Remarks 385 References 386 // Ch. 12. Inference and the Structural Model for ANOVA and MANOVA 389 // D. A. S. Fraser // 1. ANOVA: the regression model 391 // 2. MANOVA: multivariate regression model 398 References 406 // Ch. 13. Inference Based on Conditionally Specified ANOVA Models Incorporating Preliminary Testing 407 T. A. Bancroft and C.-P. Han // 1. Introduction and definitions 407 // 2. Historical remarks 413 // 3. Random ANOVA models for classified data 416 // 4. Fixed ANOVA models for classified data 426 // 5. Conditionally specified regression models 433 References 440 // Ch. 14. Quadratic Forms in Normal Variables 443 C. G. Khatri // 1. Introduction 443 // 2. Notations 444 // 3. Preliminary results 446 // 4. Necessary and sufficient conditions for Chi-squaredness and independence 449 // 5. Exact distribution of quadratic forms 454 // 6. Asymptotic distribution of quadratic forms 459 // 7. Characterization of the distributions 463 // 8. Estimation of fixed effects 465 References 466 // Ch. 15. Generalized Inverse of Matrices and Applications to Linear // Models 471 S. K. Mitra // Part 1: Generalized inverse of matrices 471 // 1. Introduction 471 // 2. Generalized inverse of a matrix 472 // 3. Reflexive generalized inverse 476 // 4. Minimum seminorm g-inverse 476 // 5. Semileast squares inverse 477 // 6. Minimum seminorm semileast square inverse 481 // 7. Optimal inverse 482 // 8. Constrained Inverse 484 // 9. Generalized inverse of partitioned matrices 485 // 10. Intersection of vector subspaces 487 // Part 2: Statistical analysis of a linear model 489 // 11. Linear estimation in a general Gauss-Markov model 489 // 12. Tests of linear hypotheses 498 // 13. Bayes linear and minimax linear estimators 500 //

14. Best linear minimum bias estimator (BLIMBE) 505 // 15. Improved estimation: Hoerl-Kennard and James-Stein estimators 506 // 16. Specification errors in the dispersion matrix D(Y)-robustness of BLUE 508 References 509 // Ch. 16. Likelihood Ratio Tests for Mean Vectors and Covariance Matrices // 513 // P. R. Krishnaiah and J. C. Lee // 1. Introduction 513 // 2. Tests on mean vectors 514 // 3. Test on independence of sets of variates 519 // xiv // Table of contents // 4. Tests on covariance matrices 522 // 5. Tests on mean vectors and covariance matrices simultaneously 529 // 6. Test for equality of means, variances and covariances 533 // 7. Test for compound symmetry 534 // 8. Tests on linear structures of covariance matrices 535 References 568 // Ch. 17. Assessing Dimensionality in Multivariate Regression A. J. Izenman // 1. Introduction 571 // 2. Reduced-rank regression: main results 573 // 3. Residuals from a reduced-rank regression 576 // 4. The case of unknown rank 577 // 5. A simple example 578 // 6. The rank trace 580 // 7. Comparing gamma plots of multivariate residuals 587 References 590 // Ch. 18. Parameter Estimation in Nonlinear Regression Models H. Bunke // 1. Introduction 593 // 2. Examples 594 // 3. Least squares estimation 595 // 4. Linearization 598 // 5. Polynomial approximation 599 // 6. Consistency of least squares estimators 602 // 7. Asymptotic distribution of least-squares estimators 605 // 8. Asymptotic optimality of GLSE without normality 607 // 9. Maximum likelihood estimation 608 // 10. Robust nonlinear regression 611 // 11. Confidence regions 613 References 614 // Ch. 19. Early History of Multiple Comparison Tests 617 // H. L. Harter // References 621 // Ch. 20. Representations of Simultaneous Pairwise Comparisons 623 // A. R. Sampson // 1. Introduction 623 // 2. Techniques for small and moderate numbers of comparisons 624 //

3. Tabular displays for large numbers of comparisons 625 // 4. Chords in a circle 627 References 629 // Ch. 21. Simultaneous Test Procedures for Mean Vectors and Covariance Matrices 631 // P. R. Krishnaiah, G. S. Mudholkar and P. Subbaiah // 1. Introduction 631 // 2. Multiple comparisons of means 632 // 3. Roy’s largest root test and 7 ax test for multiple comparisons of mean vectors 638 // 4. Step-down procedure and finite intersection tests 641 // 5. Tests based on traces 645 // 6. Computer programs for tests on multiple comparisons of mean vectors 647 // 7. Illustration 650 // 8. Simultaneous tests for equality of the variances 653 // 9. Simultaneous tests specifying the covariance matrices 655 // 10. Simultaneous tests for the equality of the covariance matrices 656 // Appendix A. Computer programs for the largest root, trace and tests 661 // Appendix B. Computer programs for finite intersection and step-down procedures 666 References 670 // Ch. 22. Nonparametric Simultaneous Inference for some MANOVA Models 673 // P. K. Sen // 1. Introduction 673 // 2. Simultaneous inference for the one-way ANOVA models 674 // 3. Simultaneous inference in two-way ANOVA models 679 // 4. Simultaneous inference for the MANOVA models 682 // 5. Simultaneous inference in MANOCOVA problems 692 // 6. Some general remarks 695 Acknowledgments 700 References 700 // Ch. 23. Comparison of Some Computer Programs for Univariate and Multivariate Analysis of Variance 703 R. D. Bock and D. Brandt // 1. Remarks on estimation and tests of hypotheses in non-orthogonal analysis of // variance 706 // 2. Remarks on analysis of covariance and repeated measures analysis 713 // 3. Comments on two special purpose programs 719 // 4. Program summaries 722 // 5. Test Problems 735 References 742 // Ch. 24. Computations of Some Multivariate Distributions 745 P. R. Krishnaiah // 1. Introduction 745 //

2. Multivariate normal and multivariate / distributions 746 // 3. Distributions of the studentized largest and smallest chi-square distributions 749 // 4. Distributions of the range and studentized range 752 // 5. Multivariate chi-square and multivariate F distributions 753 // 6. Distributions of quadratic forms 758 // 7. Distribution of the maximum of correlated Hotelling’s T2 statistics 763 // 8. Distributions of the individual roots of a class of random matrices 764 // 9. Distributions of the ratios of the extreme roots and ratios of the individual roots to the sum of the roots 777 // 10. Distributions of the traces of multivariate beta and multivariate F matrices 779 Appendix 781 Acknowledgement 965 References 965 // Ch. 25. Inference on the Structure of Interaction in Two-Way Classification Model P. R. Krishnaiah and M. Yochmomtz // 1. Introduction 973 // 2. Some early developments on tests for additivity 974 // 3. Tests for the structure of interaction using eigenvalues of a random matrix 979 // 4. Tests for the main effects 988 // 5. Illustrative examples 990 References 992 // Subject Index 995