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Informationen zum Autor 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. Klappentext 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. Zusammenfassung An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. Inhaltsverzeichnis 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 R¿ = 0 against R¿ ¿ 0. 4.4 Tests of h(¿) = 0. 4.5 An Overview of Score Tests with no Inequality Constraints. 4.6 Local Score-type Tests of Ho : ¿ = 0 vs H1 : ¿ &epsis; ¿. 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. <...
