Constrained Statistical Inference (eBook)

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. 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.

Dedication.

Preface.

1. Introduction.

1.1 Preamble.

1.2 Examples.

1.3 Coverage and Organization of the Book.

2. Comparison of Population Means and Isotonic
Regression.

2.1 Ordered Hypothesis Involving Population Means.

2.2 Test of Inequality Constraints.

2.3 Isotonic Regression.

2.4 Isotonic Regression: Results Related to Computational
Formulas.

3. Two Inequality Constrained Tests on Normal Means.

3.1 Introduction.

3.2 Statement of Two General Testing Problems.

3.3 Theory: The Basics in 2 Dimensions.

3.4 Chi-bar-square Distribution.

3.5 Computing the Tail Probabilities of chi-bar-square
Distributions.

3.6 Detailed Results relating to chi-bar-square
Distributions.

3.7 LRT for Type A Problems: V is known.

3.8 LRT for Type B Problems: V is known.

3.9 Inequality Constrained Tests in the Linear Model.

3.10 Tests When V is known.

3.11 Optimality Properties.

3.12 Appendix 1: Convex Cones.

3.13 Appendix B. Proofs.

4. Tests in General Parametric Models.

4.1 Introduction.

2.2 Preliminaries.

4.3 Tests of Rtheta = 0 against Rtheta >= 0.

4.4 Tests of h(theta) = 0.

4.5 An Overview of Score Tests with no Inequality
Constraints.

4.6 Local Score-type Tests of Ho : psi = 0 vs
H1 : psi &epsis; Psi.

4.7 Approximating Cones and Tangent Cones.

4.8 General Testing Problems.

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

5. Likelihood and Alternatives.

5.1 Introduction.

5.2 The Union-Intersection principle.

5.3 Intersection Union Tests (IUT).

5.4 Nanparametrics.

5.5 Restricted Alternatives and Simes-type Procedures.

5.6 Concluding Remarks.

6. Analysis of Categorical Data.

6.1 Motivating Examples.

6.2 Independent Binomial Samples.

6.3 Odds Ratios and Monotone Dependence.

6.4 Analysis of 2 x c Contingency Tables.

6.5 Test to Establish that Treatment is Better than Control.

6.6 Analysis of r x c Tables.

6.7 Square Tables and Marginal Homogeneity.

6.8 Exact Conditional Tests.

6.9 Discussion.

7. Beyond Parametrics.

7.1 Introduction.

7.2 Inference on Monotone Density Function.

7.3 Inference on Unimodal Density Function.

7.4 Inference on Shape Constrained Hazard Functionals.

7.5 Inference on DMRL Functions.

7.6 Isotonic Nonparametric Regression: Estimation.

7.7 Shape Constraints: Hypothesis Testing.

8. Bayesian Perspectives.

8.1 Introduction.

8.2 Statistical Decision Theory Motivations.

8.3 Stein's Paradox and Shrinkage Estimation.

8.4 Constrained Shrinkage Estimation.

8.5 PC and Shrinkage Estimation in CSI.

8.6 Bayes Tests in CSI.

8.7 Some Decision Theoretic Aspects: Hypothesis Testing.

9. Miscellaneous Topics.

9.1 Two-sample Problem with Multivariate Responses.

9.2 Testing that an Identified Treatment is the Best: The
mini-test.

9.3 Cross-over Interaction.

9.4 Directed Tests.

Bibliography.

Index.

"This monograph provides an excellent coverage of the last twenty
years of constrained statistical inference." (Journal of the
American Statistical Association, March 2006)

"...an invaluable resource for any researcher with interests
in constrained problems...it is easy to conclude that any
statistical library would be incomplete without it."
(Biometrics, December 2005)

"...a valuable source of information for statisticians
working in any area..." (Mathematical Reviews,
2005k)