Cuadras / Rao Multivariate Analysis: Future Directions 2

1. Auflage 2014
ISBN: 978-1-4832-9756-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 5, 494 Seiten, Web PDF

Reihe: North-Holland Series in Statistics and Probability

The contributions in this volume, made by distinguished statisticians in several frontier areas of research in multivariate analysis, cover a broad field and indicate future directions of research. The topics covered include discriminant analysis, multidimensional scaling, categorical data analysis, correspondence analysis and biplots, association analysis, latent variable models, bootstrap distributions, differential geometry applications and others. Most of the papers propose generalizations or new applications of multivariate analysis.This volume will be of great interest to statisticians, probabilists, data analysts and scientists working in the disciplines such as biology, biometry, ecology, medicine, econometry, psychometry and marketing. It will be a valuable guide to professors, researchers and graduate students seeking new and promising lines of statistical research.

Autoren/Hrsg.

Cuadras, C. M.

Rao, C. R.

Inhaltsverzeichnis

1;Front Cover
;1
2;Multivariate Analysis: Future Directions 2;4
3;Copyright Page;5
4;Dedication;6
5;Preface;8
6;Table of Contents;10
7;List of contributors;14
8;PART 1: Discriminant analysis and scaling;18
8.1;Chapter 1. Discriminant analysis for mixed variables: Integrating trees and regression models;20
8.1.1;Abstract;20
8.1.2;1. Introduction;20
8.1.3;2. The RECPAM approach in general;22
8.1.4;3. RECPAM and the multivariate model;25
8.1.5;4. Direct applications;27
8.1.6;5. Discriminant analysis with variables of mixed type;32
8.1.7;6. An example;34
8.1.8;7. Summary and conclusion;35
8.1.9;References;38
8.2;Chapter 2. A strong Lagrangian look at profile log likelihood with applications to linear discrimination;40
8.2.1;Abstract;40
8.2.2;1. Introduction;40
8.2.3;2. An example;43
8.2.4;3. Preliminaries;44
8.2.5;4. Relaxation of condition (4);48
8.2.6;5. Removal of condition (4);50
8.2.7;6. Application to linear discrimination;52
8.2.8;7. Examples;55
8.2.9;8. Further work;56
8.2.10;9. Appendix;58
8.2.11;References;61
8.3;Chapter 3. Continuous metric scaling and prediction;64
8.3.1;Abstract;64
8.3.2;1. Introduction;64
8.3.3;2. Discrete metric scaling;66
8.3.4;3. Distance-based prediction;72
8.3.5;4. Continuous metric scaling;74
8.3.6;5. Continuous prediction;78
8.3.7;6. Conclusions;81
8.3.8;References;81
8.4;Chapter 4. A comparison of techniques for finding components with simple structure;84
8.4.1;Abstract;84
8.4.2;Introduction;84
8.4.3;1. Theoretical comparison of techniques for finding simply structuredcomponents;86
8.4.4;2. Empirical comparison of techniques for finding simply structuredcomponents;90
8.4.5;3. Analysis of an empirical data set;100
8.4.6;4. Discussion;101
8.4.7;References;103
8.5;Chapter 5. Antedependence modelling in discriminant analysis of high-dimensional spectroscopic data;104
8.5.1;Abstract;104
8.5.2;1. Introduction;104
8.5.3;2. Antedependence modelling;106
8.5.4;3. Computer Implementation;108
8.5.5;4. Applications and comparisons;109
8.5.6;5. Conclusion;111
8.5.7;Acknowledgement;111
8.5.8;References;111
8.6;Chapter 6. On scaling of ordinal categorical data;114
8.6.1;Abstract;114
8.6.2;1. Introduction;114
8.6.3;2. Comparison of treatments: ANOVA techniques;116
8.6.4;3. Scaling of categories in a multidimensional contingency table;124
8.6.5;4. Scaling of ordinal categories in a mixed set-up;125
8.6.6;5. Acknowledgement;126
8.6.7;6. Appendix;126
8.6.8;References;126
9;PART 2: Latent variable models;128
9.1;Chapter 7. Instrumental variable estimation for nonlinear factor analysis;130
9.1.1;Abstract;130
9.1.2;1. Introduction;130
9.1.3;2. Identification;132
9.1.4;3. Instrumental variable estimation;134
9.1.5;4. A numerical example;142
9.1.6;5. Derivations;143
9.1.7;References;145
9.2;Chapter 8. The analysis of panel data with mean andcovariance structure models for non-metricdependent variables;148
9.2.1;1. Specification and estimation of mean and covariance structures fornon-metric variables;148
9.2.2;2. Models for non-metric panel data;153
9.2.3;3. A state dependence model for employment status;161
9.2.4;References;167
9.3;Chapter 9. The geometry of mean or covariance structuremodels in multivariate normal distributions:A unified approach;170
9.3.1;Abstract;170
9.3.2;1. Introduction;170
9.3.3;2. Review and notation;171
9.3.4;3. Regression model;173
9.3.5;4. Covariance structure model;176
9.3.6;5. Discussion;186
9.3.7;References;186
9.4;Chapter 10. Structured latent curve models;188
9.4.1;Abstract;188
9.4.2;1. Introduction;188
9.4.3;2. The latent curve model;189
9.4.4;3. Characteristics of the data;190
9.4.5;4. Development of structured latent curve models;193
9.4.6;5. Specific structured latent curve models;195
9.4.7;6. Effect of reparametrization;199
9.4.8;7. Joint model for trials and concomitant variables;201
9.4.9;8. Fitting the model;203
9.4.10;9. Application;205
9.4.11;10. Robustness considerations;210
9.4.12;11. Acknowledgement;212
9.4.13;References;212
9.5;Chapter 11. Latent variable modeling of growth with missing dataand multilevel data;216
9.5.1;Abstract;216
9.5.2;1. Introduction;216
9.5.3;2. A general latent variable framework;217
9.5.4;3. A motivating example;218
9.5.5;4. Modeling of individual differences in growth;219
9.5.6;5. Modeling of missing data;221
9.5.7;6. Modeling of multilevel data;223
9.5.8;7. Discussion;226
9.5.9;References;226
9.6;Chapter 12. Asymptotic robust inferences in multi-sampleanalysis of augmented-moment structures;228
9.6.1;Abstract;228
9.6.2;1. Introduction;228
9.6.3;2. Multi-sample analysis of second-order moment structures: asymptotictheory;230
9.6.4;3. Asymptotic robustness;237
9.6.5;4. Illustration;241
9.6.6;References;244
10;PART 3: Correspondence analysis and relatedtopics;248
10.1;Chapter 13. Multiple Correspondence Analysis on panel data;250
10.1.1;Abstract;250
10.1.2;1. Introduction;250
10.1.3;2. The panel data;251
10.1.4;3. Analysis by concatenation of tables;252
10.1.5;4. Analysis of the average table;254
10.1.6;5. Analysis of the tendency;255
10.1.7;6. Local Multiple Correspondence Analysis;255
10.1.8;7. LMCA to panel data;258
10.1.9;8. Equivalence with Conditional Multiple Correspondence Analysis;259
10.1.10;References;261
10.2;Chapter 14. Analysing dependence in largecontingency tables: Dimensionality and patternsin scatter-plots;262
10.2.1;Abstract;262
10.2.2;1. Introduction;262
10.2.3;2. Models;263
10.2.4;3. Estimation;266
10.2.5;4. Biplots;268
10.2.6;5. Example;269
10.2.7;6. Latent normal distribution and association models;272
10.2.8;7. Latent normal distribution and correlation models;274
10.2.9;References;278
10.3;Chapter 15. Correspondence analysis, association analysis, andgeneralized nonindependence analysis of contingencytables: Saturated and unsaturated models, andappropriate graphical displays;282
10.3.1;Abstract;282
10.3.2;1. Introduction and summary;283
10.3.3;2. Correspondence analysis;284
10.3.4;3. Unweighted and weighted association analysis;286
10.3.5;4. Generalized nonindependence analysis;289
10.3.6;5. Graphical displays;296
10.3.7;6. Saturated models and unsaturated models;307
10.3.8;Appendix;309
10.3.9;References;310
10.4;Chapter 16. Recent advances in biplot methodology;312
10.4.1;Abstract;312
10.4.2;1. Introduction;312
10.4.3;2. The geometry of linear biplots;317
10.4.4;3. Non-linear biplots;324
10.4.5;4. Generalised biplots and categorical variables;330
10.4.6;5. Relationship of non-linear to generalised biplots;334
10.4.7;6. Conclusion;335
10.4.8;Appendix. Derivation of algebraic formulae and other results forback-projection;337
10.4.9;References;341
10.5;Chapter 17. Multivariate generalisations of correspondenceanalysis;344
10.5.1;Abstract;344
10.5.2;1. Introduction;344
10.5.3;2. Simple correspondence analysis;345
10.5.4;3. CA of concatenated tables;347
10.5.5;4. CA of super-indicator matrix and Burt matrix;349
10.5.6;5. CA of modified Burt matrices;350
10.5.7;6. CA of Burt matrix with diagonal matrices missing;351
10.5.8;7. Rescaled MCA;352
10.5.9;8. An example;354
10.5.10;9. Discussion and conclusion;356
10.5.11;References;356
10.6;Chapter 18. Correspondence analysis and classification;358
10.6.1;1. Introduction;358
10.6.2;2. Some links between the two approaches;359
10.6.3;3. Eigenvalues and indices;365
10.6.4;4. Some hybrid methods;369
10.6.5;5. Complementarity from a practical point of view;371
10.6.6;References;372
10.7;Chapter 19. Some generalizations of correspondence analysis;376
10.7.1;Abstract;376
10.7.2;1. Introduction;376
10.7.3;2. Formalism;378
10.7.4;3. Linearizing the regressions;379
10.7.5;4. Maximizing the correlation;380
10.7.6;5. More than two variables;381
10.7.7;6. Strained multinomials;382
10.7.8;7. Some questions;383
10.7.9;8. LPV diagonalization;383
10.7.10;9. Functions of correlation coefficients;386
10.7.11;10. Consequences of bi-linearizability;387
10.7.12;11. Model oriented approach;388
10.7.13;12. Two-step techniques;388
10.7.14;References;390
11;PART 4: Differential geometry applications;394
11.1;Chapter 20. Differential geometry of estimating functions;396
11.1.1;Abstract;396
11.1.2;1. Estimating functions;396
11.1.3;2. Decomposition of tangent bundles;397
11.1.4;3. Answers to fundamental questions;398
11.1.5;References;400
11.2;Chapter 21. Statistical inference and differential geometry —Some recent developments;402
11.2.1;Abstract;402
11.2.2;1. Introduction;402
11.2.3;2. An adjusted profile likelihood and embedding curvature;404
11.2.4;3. Yokes and symplectic geometry;407
11.2.5;4. Orthogeodesic models;411
11.2.6;References;412
11.3;Chapter 22. Random variables, integral curves and estimation of probabilities;414
11.3.1;Abstract;414
11.3.2;1. Introduction;414
11.3.3;2. Random variables and integral curves;415
11.3.4;3. Modification of probabilities;417
11.3.5;4. Density functions;421
11.3.6;5. Acknowledgement;422
11.3.7;References;422
11.4;Chapter 23. Sufficient geometrical conditions for Cramer-Raoinequality;424
11.4.1;Abstract;424
11.4.2;1. Introduction;424
11.4.3;2. Frechet differentiability on Lebesgue spaces;425
11.4.4;3. Regular models;428
11.4.5;4. The mean value theorem;431
11.4.6;5. The Cramer-Rao inequality;434
11.4.7;References;437
11.5;Chapter 24. On an intrinsic analysis of statistical estimation;438
11.5.1;Abstract;438
11.5.2;1. Introduction;438
11.5.3;2. The Riemannian geometry of statistical models;444
11.5.4;3. Lower bound of mean square Rao distance for intrinsically unbiasedestimators;447
11.5.5;4. Conditional mean values of manifold valued random objects;449
11.5.6;5. Global estimator efficiency;450
11.5.7;6. Discussion;452
11.5.8;References;453
12;PART 5: Bootstrap, conditional models anddivergences;456
12.1;Chapter 25. Conditionally specified models: Structure andinference;458
12.1.1;Abstract;458
12.1.2;1. Conditionally specified models;458
12.1.3;2. Alternative conditional specification paradigms;462
12.1.4;3. Parameter estimation in unconditionally specified models;465
12.1.5;4. Multivariate extensions;466
12.1.6;References;467
12.2;Chapter 26. Multivariate analysis in the computer age;468
12.2.1;Abstract;468
12.2.2;1. Introduction;468
12.2.3;2. Bootstrap methods;469
12.2.4;3. BCa intervals;471
12.2.5;4. ABC intervals;474
12.2.6;5. Calibration;477
12.2.7;6. Missing data;481
12.2.8;7. Bayes and likelihood calculations;484
12.2.9;8. Appendix;487
12.2.10;References;487
12.3;Chapter 27. Chapter New parametric measures of information based ongeneralized ^-divergences;490
12.3.1;Abstract;490
12.3.2;1. Introduction;490
12.3.3;2. Information matrices associated to parameter perturbance;492
12.3.4;3. Information matrices associated to differential metrics;496
12.3.5;4. Parametric measures of information;499
12.3.6;5. Asymptotic distribution;501
12.3.7;References;504