Constrained Statistical Inference: Inequality, Order, and Shape Restrictions
Constrained Statistical Inference: Inequality, Order, and Shape Restrictions
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DOI：
10.1002/9781118165614
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发表时间：
2001-10
期刊：
影响因子：
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通讯作者：
M. Silvapulle;P. Sen
中科院分区：
文献类型：
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作者：
M. Silvapulle;P. Sen
奉献精神。前言。1.引言。1.1序言。1.2个例子。1.3本书的覆盖面和组织。2.总体均值与保序回归的比较。2.1涉及总体平均数的有序假设。2.2不等约束的检验。2.3等张回归。2.4等张回归：与计算公式有关的结果。3.关于正态均值的两个不等式约束检验。3.1引言。3.2两个一般测试问题的陈述。3.3理论：2维的基础知识。3.4卡方分布。3.5计算卡方分布的尾概率。3.6关于卡方分布的详细结果。3.7 A类问题的轻铁：V是已知的。3.8 B类问题的轻铁：V是已知的。3.9线性模型中的不等式约束检验。3.10已知V时进行测试。3.11最优属性。3.12附录1：凸锥。3.13附录B校样。4.在通用参数模型中进行试验。4.1引言。2.2预备期。4.3 Rtheta=0对Rtheta 0的测试。4.4 h(Theta)=0的检验。4.5没有不平等限制的分数测试概述。4.6 HO：PSI=0与H1：PSI PSI的本地分数类型测试。4.7近似圆锥体和切圆锥体。4.8一般测试问题。4.9当True Value在边界上时，MLE的属性。5.可能性和替代方案。5.1引言。5.2并集-交集原则。5.3交叉点联合试验(IUT)。5.4纳米参数。5.5受限替代方案和SIMES类型的程序。5.6结束语。6.分类数据分析。6.1鼓舞人心的例子。6.2独立二项样本。6.3赔率比和单调依赖。6.4 2xc列联表的分析。6.5进行试验，以确定处理效果优于对照。6.6 R×C表的分析。6.7方桌和边际同质性。6.8精确条件测验。6.9讨论。7.超越参数。7.1引言。7.2单调密度函数的推论。7.3单峰密度函数的推论。7.4形状约束危险泛函的推论。7.5关于DMRL函数的推理。7.6保序非参数回归：估计。7.7形状约束：假设检验。8.贝叶斯观点。8.1引言。8.2统计决策理论动机。8.3斯泰因悖论和收缩估计。8.4约束收缩估计。8.5PC和CSI中的收缩估计。8.6 CSI中的贝叶斯测试。8.7一些决策理论方面：假设检验。9.其他主题。9.1具有多变量响应的两样本问题。9.2测试确定的治疗是最好的：迷你测试。9.3交叉互动。9.4定向测试。参考书目。索引。
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 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.