Constrained Statistical Inference Order, Inequality, and Shape Constraints
by Silvapulle, Mervyn J.; Sen, Pranab KumarEdition: 1st
Format: Hardcover
Pub. Date: 2004-11-08
Publisher(s): Wiley-Interscience
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Summary
This volumes focuses on the theory of statistical inference under inequality constraints, providing a unified and up-to-date treatment of the methodology. The scope of applications of the presented methodology and theory in different fields is clearly illustrated by using examples from several areas, especially sociology, econometrics, and biostatistics. The authors also discuss a broad range of other inequality constrained inference problems, which do not fit well in the contemplated unified framework, providing meaningful access to comprehend methodological resolutions.
Author Biography
MERVYN J. SILVAPULLE, PhD, is an Associate Professor in the Department of Statistical Science at La Trobe University in Bundoora, Australia. He received his PhD in statistics from the Australian National University in 1981. <BR> |PRANAB K. SEN, PhD, is a Professor in the Departments of Biostatistics and Statistics and Operations Research at the University of North Carolina at Chapel Hill. He received his PhD in 1962 from Calcutta University, India.
Table of Contents
| Dedication | p. v |
| Preface | p. xv |
| Introduction | p. 1 |
| Preamble | p. 1 |
| Examples | p. 2 |
| Coverage and Organization of the Book | p. 23 |
| Comparison of Population Means and Isotonic Regression | p. 25 |
| Ordered Alternative Hypotheses | p. 27 |
| Ordered Null Hypotheses | p. 38 |
| Isotonic Regression | p. 42 |
| Isotonic Regression: Results Related to Computational Formulas | p. 46 |
| Appendix: Proofs | p. 53 |
| Problems | p. 57 |
| Tests on Multivariate Normal Mean | p. 59 |
| Introduction | p. 59 |
| Statement of Two General Testing Problems | p. 60 |
| Theory: The Basics in Two Dimensions | p. 63 |
| Chi-bar-square Distribution | p. 75 |
| Computing the Tail Probabilities of Chi-bar-square Distributions | p. 78 |
| Results on Chi-bar-square Weights | p. 81 |
| LRT for Type A problems: V is Known | p. 83 |
| LRT for Type B problems: V is Known | p. 90 |
| Tests on the Linear Regression Parameter | p. 95 |
| Tests When V is Unknown (Perlman's Test and Alternatives) | p. 100 |
| Optimality Properties | p. 107 |
| Appendix 1: Convex Cones, Polyhedrals, and Projections | p. 111 |
| Appendix 2: Proofs | p. 125 |
| Problems | p. 133 |
| Tests in General Parametric Models | p. 143 |
| Introduction | p. 143 |
| Preliminaries | p. 145 |
| Tests of R[theta] = 0 Against R[theta greater than or equal] 0 | p. 148 |
| Tests of h([theta]) = 0 | p. 164 |
| An Overview of Score Tests with no Inequality Constraints | p. 168 |
| Local Score-type Tests of H[subscript 0] : [psi] = 0 Against H[subscript 1] : [psi set membership Psi] | p. 175 |
| Approximating Cones and Tangent Cones | p. 183 |
| General Testing Problems | p. 194 |
| Properties of the mle When the True Value is on the Boundary | p. 209 |
| Appendix: Proofs | p. 215 |
| Likelihood and Alternatives | p. 221 |
| Introduction | p. 221 |
| The Union-Intersection Principle | p. 222 |
| Intersection Union Tests (IUT) | p. 235 |
| Nonparametrics | p. 243 |
| Restricted Alternatives and Simes-type Procedures | p. 264 |
| Concluding Remarks | p. 275 |
| Problems | p. 276 |
| Analysis of Categorical Data | p. 283 |
| Introduction | p. 283 |
| Motivating Examples | p. 285 |
| Independent Binomial Samples | p. 292 |
| Odds Ratios and Monotone Dependence | p. 298 |
| Analysis of 2 x c contingency tables | p. 306 |
| Test to Establish that Treatment is Better Than Control | p. 313 |
| Analysis of r x c Tables | p. 315 |
| Square Tables and Marginal Homogeneity | p. 322 |
| Exact Conditional Tests | p. 324 |
| Discussion | p. 335 |
| Proofs | p. 335 |
| Problems | p. 338 |
| Beyond Parametrics | p. 345 |
| Introduction | p. 345 |
| Inference on Monotone Density Function | p. 346 |
| Inference on Unimodal Density Function | p. 354 |
| Inference on Shape-Constrained Hazard Functionals | p. 357 |
| Inference on DMRL Functions | p. 362 |
| Isotonic Nonparametric Regression: Estimation | p. 366 |
| Shape Constraints: Hypothesis Testing | p. 369 |
| Problems | p. 374 |
| Bayesian Perspectives | p. 379 |
| Introduction | p. 379 |
| Statistical Decision Theory Motivations | p. 380 |
| Stein's Paradox and Shrinkage Estimation | p. 384 |
| Constrained Shrinkage Estimation | p. 388 |
| PCC and Shrinkage Estimation in CSI | p. 396 |
| Bayes Tests in CSI | p. 400 |
| Some Decision Theoretic Aspects: Hypothesis Testing | p. 402 |
| Problems | p. 404 |
| Miscellaneous Topics | p. 407 |
| Two-sample Problem with Multivariate Responses | p. 408 |
| Testing that an Identified Treatment is the Best: the Min Test | p. 422 |
| Cross-over Interaction | p. 434 |
| Directed Tests | p. 455 |
| Problems | p. 463 |
| Bibliography | p. 469 |
| Index | p. 525 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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