Constrained statistical inference : inequality, order, and shape restrictions / Mervyn J. Silvapulle, Pranab K. Sen.

Format:

Book

Author/Creator:

Silvapulle, Mervyn J., 1951-

Contributor:

Sen, Pranab Kumar, 1937-2023

Simon Nelson Patten Fund.

Series:

Wiley series in probability and statistics

Language:

English

Subjects (All):

Multivariate analysis.

Physical Description:

xvii, 532 pages : illustrations ; 24 cm.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2005]

Contents:

1.3 Coverage and Organization of the Book 23

2 Comparison of Population Means and Isotonic Regression 25

2.1 Ordered Alternative Hypotheses 27

2.2 Ordered Null Hypotheses 38

2.3 Isotonic Regression 42

2.4 Isotonic Regression: Results Related to Computational Formulas 46

3 Tests on Multivariate Normal Mean 59

3.2 Statement of Two General Testing Problems 60

3.3 Theory: The Basics in Two Dimensions 63

3.4 Chi-bar-square Distribution 75

3.5 Computing the Tail Probabilities of Chi-bar-square Distributions 78

3.6 Results on Chi-bar-square Weights 81

3.7 LRT for Type A problems: V is Known 83

3.8 LRT for Type B problems: V is Known 90

3.9 Tests on the Linear Regression Parameter 95

3.10 Tests When V is Unknown (Perlman's Test and Alternatives) 100

3.11 Optimality Properties 107

3.12 Appendix 1: Convex Cones, Polyhedrals, and Projections 111

4 Tests in General Parametric Models 143

4.3 Tests of R[theta] = 0 Against R[theta greater than or equal] 0 148

4.4 Tests of h([theta]) = 0 164

4.5 An Overview of Score Tests with no Inequality Constraints 168

4.6 Local Score-type Tests of H[subscript 0] : [psi] = 0 Against H[subscript 1] : [psi set membership Psi] 175

4.7 Approximating Cones and Tangent Cones 183

4.8 General Testing Problems 194

4.9 Properties of the mle When the True Value is on the Boundary 209

5 Likelihood and Alternatives 221

5.2 The Union-Intersection Principle 222

5.3 Intersection Union Tests (IUT) 235

5.4 Nonparametrics 243

5.5 Restricted Alternatives and Simes-type Procedures 264

6 Analysis of Categorical Data 283

6.2 Motivating Examples 285

6.3 Independent Binomial Samples 292

6.4 Odds Ratios and Monotone Dependence 298

6.5 Analysis of 2 x c contingency tables 306

6.6 Test to Establish that Treatment is Better Than Control 313

6.7 Analysis of r x c Tables 315

6.8 Square Tables and Marginal Homogeneity 322

6.9 Exact Conditional Tests 324

6.11 Proofs 335

7 Beyond Parametrics 345

7.2 Inference on Monotone Density Function 346

7.3 Inference on Unimodal Density Function 354

7.4 Inference on Shape-Constrained Hazard Functionals 357

7.5 Inference on DMRL Functions 362

7.6 Isotonic Nonparametric Regression: Estimation 366

7.7 Shape Constraints: Hypothesis Testing 369

8 Bayesian Perspectives 379

8.2 Statistical Decision Theory Motivations 380

8.3 Stein's Paradox and Shrinkage Estimation 384

8.4 Constrained Shrinkage Estimation 388

8.5 PCC and Shrinkage Estimation in CSI 396

8.6 Bayes Tests in CSI 400

8.7 Some Decision Theoretic Aspects: Hypothesis Testing 402

9.1 Two-sample Problem with Multivariate Responses 408

9.2 Testing that an Identified Treatment is the Best: the Min Test 422

9.3 Cross-over Interaction 434

9.4 Directed Tests 455.

Notes:

Includes bibliographical references (pages 469-524) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Simon Nelson Patten Fund.

Presented by The American Academy of Political and Social Science in memory of Simon Nelson Patten; 2004/2005

ISBN:

0471208272

OCLC:

55000352

Online:

Publisher description