Constrained Statistical Inference
Order, Inequality, and Shape Constraints
Published on 15. September 2011
532 pages
978-1-118-16563-8 (ISBN)
Description
An up-to-date approach to understanding statistical inference
Statistical inference is finding useful applications in numerousfields, from sociology and econometrics to biostatistics. Thisvolume enables professionals in these and related fields to masterthe concepts of statistical inference under inequality constraintsand to apply the theory to problems in a variety of areas.
Constrained Statistical Inference: Order, Inequality, and ShapeConstraints provides a unified and up-to-date treatment of themethodology. It clearly illustrates concepts with practicalexamples from a variety of fields, focusing on sociology,econometrics, and biostatistics.
The authors also discuss a broad range of otherinequality-constrained inference problems that do not fit well inthe contemplated unified framework, providing a meaningful way forreaders to comprehend methodological resolutions.
Chapter coverage includes:
* Population means and isotonic regression
* Inequality-constrained tests on normal means
* Tests in general parametric models
* Likelihood and alternatives
* Analysis of categorical data
* Inference on monotone density function, unimodal densityfunction, shape constraints, and DMRL functions
* Bayesian perspectives, including Stein's Paradox,shrinkage estimation, and decision theory
Reviews / Votes
"This monograph provides an excellent coverage of the last twentyyears of constrained statistical inference." (Journal of theAmerican Statistical Association, March 2006) "...an invaluable resource for any researcher with interestsin constrained problems...it is easy to conclude that anystatistical library would be incomplete without it."(Biometrics, December 2005) "...a valuable source of information for statisticiansworking in any area..." (Mathematical Reviews,2005k)More details
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Software
09/2011
Wiley
€204.19
Shipment within 15-20 days
Mervyn J. Silvapulle | Pranab Kumar Sen
Constrained Statistical Inference
Order, Inequality, and Shape Constraints
Book
11/2004
Wiley
€175.50
Shipment within 10-20 days
Persons
MERVYN J. SILVAPULLE, PhD, is an Associate Professor in theDepartment of Statistical Science at La Trobe University inBundoora, Australia. He received his PhD in statistics from theAustralian National University in 1981.
PRANAB K. SEN, PhD, is a Professor in the Departments ofBiostatistics and Statistics and Operations Research at theUniversity of North Carolina at Chapel Hill. He received his PhD in1962 from Calcutta University, India.
Content
Dedication.
Preface.
1. Introduction.
1.1 Preamble.
1.2 Examples.
1.3 Coverage and Organization of the Book.
2. Comparison of Population Means and IsotonicRegression.
2.1 Ordered Hypothesis Involving Population Means.
2.2 Test of Inequality Constraints.
2.3 Isotonic Regression.
2.4 Isotonic Regression: Results Related to ComputationalFormulas.
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-squareDistributions.
3.6 Detailed Results relating to chi-bar-squareDistributions.
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 InequalityConstraints.
4.6 Local Score-type Tests of Ho : psi = 0 vsH1 : 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 theBoundary.
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: Themini-test.
9.3 Cross-over Interaction.
9.4 Directed Tests.
Bibliography.
Index.
