Constrained Statistical Inference : Order, Inequality, and Shape Constraints
Mervyn J. Silvapulle
Bok Engelsk 2011 · Electronic books.
| Annen tittel | |
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| Utgitt | Hoboken : : Wiley, , 2011.
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| Omfang | 1 online resource (560 p.)
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| Opplysninger | Description based upon print version of record.. - Constrained Statistical Inference: Inequality, Order, and Shape Restrictions; Dedication; Contents; 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 Alternative Hypotheses; 2.1.1 Test of H0 : μ1 = μ2 = μ3 Against an Order Restriction; 2.1.2 Test of H0 = μ1 = ... = μk Against an Order Restriction; 2.1.2.1 Exact finite sample results when the error distribution is N(0, σ2); 2.1.2.2 Computing minμεH1 Σ Σ(yij - μi)2, F, and E2; 2.1.3 General Remarks; 2.2 Ordered Null Hypotheses. - 2.3 Isotonic Regression2.3.1 Quasi-order and Isotonic Regression; 2.4 Isotonic Regression: Results Related to Computational Formulas; 2.4.1 Isotonic Regression Under Simple Order; 2.4.2 Ordered Means of Exponential Family; 2.5 Appendix: Proofs; Problems; 3 Tests on Multivariate Normal Mean; 3.1 Introduction; 3.2 Statement of Two General Testing Problems; 3.2.1 Reduction by Sufficiency; 3.3 Theory: The Basics in Two Dimensions; 3.4 Chi-bar-square Distribution; 3.5 Computing the Tail Probabilities of Chi-bar-square Distributions; 3.6 Results on Chi-bar-square Weights. - 3.13 Appendix 2: ProofsProblems; 4 Tests in General Parametric Models; 4.1 Introduction; 4.2 Preliminaries; 4.3 Tests of Rθ = 0 Against Rθ >= 0; 4.3.1 Likelihood Ratio Test with iid Observations; 4.3.2 Tests in the Presence of Nuisance Parameters; 4.3.3 Wald- and Score-type Tests with iid Observations; 4.3.4 Independent Observations with Covariates; 4.3.5 Examples; 4.4 Tests of h(θ) = 0; 4.4.1 Test of h(θ) = 0 Against h(θ) >= 0; 4.4.2 Test of h(θ) = 0 Against h2(θ) >= 0; 4.5 An Overview of Score Tests with no Inequality Constraints; 4.5.1 Test of H0 : θ = θ0 Against H2 : θ = θ0. - 3.7 LRT for Type A problems: V is Known3.8 LRT for Type B problems: V is Known; 3.9 Tests on the Linear Regression Parameter; 3.9.1 Null Distributions; 3.10 Tests When V is Unknown (Perlman's Test and Alternatives); 3.10.1 Type A Testing Problem; 3.10.2 Type B Testing Problem; 3.10.3 Conditional Tests of H0 : θ = 0 vs H1 : θ >= 0; 3.11 Optimality Properties; 3.11.1 Consistency of Tests; 3.11.2 Monotonicity of the Power Function; 3.12 Appendix 1: Convex Cones, Polyhedrals, and Projections; 3.12.1 Introduction; 3.12.2 Projections onto Convex Cones; 3.12.3 Polyhedral Cones. - 4.5.2 Test of H0 : φ = φ0 Against H2 : φ = φ04.5.3 Tests Based on Estimating Equations; 4.6 Local Score-type Tests of H0 : φ = 0 Against H1 : φ ε Ψ; 4.6.1 Local Score Test of H0 : θ = 0 Against H1 : θ ε C; 4.6.2 Local Score Test of H0 : φ = 0 Against H1 : φ ε C; 4.6.3 Local Sore-Type Test Based on Estimating Equations; 4.6.4 A General Local Score-Type Test of H0 : φ = 0; 4.6.5 A Simple One-Dimensional Test of φ = 0 Against φ ε C; 4.6.6 A Data Example: Test Against ARCH Effect in an ARCH Model; 4.7 Approximating Cones and Tangent Cones; 4.7.1 Chernoff Regularity; 4.8 General Testing Problems. - 4.8.1 Likelihood Approach When Θ is Open. - An up-to-date approach to understanding statistical inference Statistical inference is finding useful applications in numerous fields, from sociology and econometrics to biostatistics. This volume enables professionals in these and related fields to master the concepts of statistical inference under inequality constraints and to apply the theory to problems in a variety of areas. Constrained Statistical Inference: Order, Inequality, and Shape Constraints provides a unified and up-to-date treatment of the methodology. It clearly illustrates concepts with practical examples from a variety of
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| Emner | |
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| Dewey | |
| ISBN | 0471208272
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