دانلود کتاب Theory of Statistical Inference

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Cover\nHalf Title\nSeries Page\nTitle Page\nCopyright Page\nContents\nPreface\n1. Distribution Theory\n 1.1. Introduction\n 1.2. Probability Measures\n 1.3. Some Important Theorems of Probability\n 1.4. Commonly Used Distributions\n 1.5. Stochastic Order Relations\n 1.6. Quantiles\n 1.7. Inversion of the CDF\n 1.8. Transformations of Random Variables\n 1.9. Moment Generating Functions\n 1.10. Moments and Cumulants\n 1.11. Problems\n2. Multivariate Distributions\n 2.1. Introduction\n 2.2. Parametric Classes of Multivariate Distributions\n 2.3. Multivariate Transformations\n 2.4. Order Statistics\n 2.5. Quadratic Forms, Idempotent Matrices and Cochran’s Theorem\n 2.6. MGF and CGF of Independent Sums\n 2.7. Multivariate Extensions of the MGF\n 2.8. Problems\n3. Statistical Models\n 3.1. Introduction\n 3.2. Parametric Families for Statistical Inference\n 3.3. Location-Scale Parameter Models\n 3.4. Regular Families\n 3.5. Fisher Information\n 3.6. Exponential Families\n 3.7. Sufficiency\n 3.8. Complete and Ancillary Statistics\n 3.9. Conditional Models and Contingency Tables\n 3.10. Bayesian Models\n 3.11. Indifference, Invariance and Bayesian Prior Distributions\n 3.12. Nuisance Parameters\n 3.13. Principles of Inference\n 3.14. Problems\n4. Methods of Estimation\n 4.1. Introduction\n 4.2. Unbiased Estimators\n 4.3. Method of Moments Estimators\n 4.4. Sample Quantiles and Percentiles\n 4.5. Maximum Likelihood Estimation\n 4.6. Confidence Sets\n 4.7. Equivariant Versus Shrinkage Estimation\n 4.8. Bayesian Estimation\n 4.9. Problems\n5. Hypothesis Testing\n 5.1. Introduction\n 5.2. Basic Definitions\n 5.3. Principles of Hypothesis Tests\n 5.4. The Observed Level of Significance (P-Values)\n 5.5. One- and Two-Sided Tests\n 5.6. Unbiasedness and Stochastic Ordering\n 5.7. Hypothesis Tests and Pivots\n 5.8. Likelihood Ratio Tests\n 5.9. Similar Tests\n 5.10. Problems\n6. Linear Models\n 6.1. Introduction\n 6.2. Linear Models – Definition\n 6.3. Best Linear Unbiased Estimators (BLUE)\n 6.4. Least Squares Estimators, BLUEs and Projection Matrices\n 6.5. Ordinary and Generalized Least Squares Estimators\n 6.6. ANOVA Decomposition and the F Test for Linear Models\n 6.7. One- and Two-Way ANOVA\n 6.8. Multiple Linear Regression\n 6.9. Constrained Least Squares Estimation\n 6.10. Simultaneous Confidence Intervals\n 6.11. Problems\n7. Decision Theory\n 7.1. Introduction\n 7.2. Ranking Estimators by MSE\n 7.3. Prediction\n 7.4. The Structure of Decision Theoretic Inference\n 7.5. Loss and Risk\n 7.6. Uniformly Minimum Risk Estimators (The Location-Scale Model)\n 7.7. Some Principles of Admissibility\n 7.8. Admissibility for Exponential Families (Karlin’s Theorem)\n 7.9. Bayes Decision Rules\n 7.10. Admissibility and Optimality\n 7.11. Problems\n8. Uniformly Minimum Variance Unbiased (UMVU) Estimation\n 8.1. Introduction\n 8.2. Definition of UMVUE’s\n 8.3. UMVUE’s and Sufficiency\n 8.4. Methods of Deriving UMVUEs\n 8.5. Nonparametric Estimation and U-statistics\n 8.6. Rank Based Measures of Correlation\n 8.7. Problems\n9. Group Structure and Invariant Inference\n 9.1. Introduction\n 9.2. MRE Estimators for Location Parameters\n 9.3. MRE Estimators for Scale Parameters\n 9.4. Invariant Density Families\n 9.5. Some Applications of Invariance\n 9.6. Invariant Hypothesis Tests\n 9.7. Problems\n10. The Neyman-Pearson Lemma\n 10.1. Introduction\n 10.2. Hypothesis Tests as Decision Rules\n 10.3. Neyman-Pearson (NP) Tests\n 10.4. Monotone Likelihood Ratios (MLR)\n 10.5. The Generalized Neyman-Pearson Lemma\n 10.6. Invariant Hypothesis Tests\n 10.7. Permutation Invariant Tests\n 10.8. Problems\n11. Limit Theorems\n 11.1. Introduction\n 11.2. Limits of Sequences of Random Variables\n 11.3. Limits of Expected Values\n 11.4. Uniform Integrability\n 11.5. The Law of Large Numbers\n 11.6. Weak Convergence\n 11.7. Multivariate Extensions of Limit Theorems\n 11.8. The Continuous Mapping Theorem\n 11.9. MGFs, CGFs and Weak Convergence\n 11.10. The Central Limit Theorem for Triangular Arrays\n 11.11. Weak Convergence of Random Vectors\n 11.12. Problems\n12. Large Sample Estimation — Basic Principles\n 12.1. Introduction\n 12.2. The -Method\n 12.3. Variance Stabilizing Transformations\n 12.4. The -Method and Higher-Order Approximations\n 12.5. The Multivariate -Method\n 12.6. Approximating the Distributions of Sample Quantiles: The Bahadur Representation Theorem\n 12.7. A Central Limit Theorem for U-statistics\n 12.8. The Information Inequality\n 12.9. Asymptotic Efficiency\n 12.10. Problems\n13. Asymptotic Theory for Estimating Equations\n 13.1. Introduction\n 13.2. Consistency and Asymptotic Normality of M-Estimators\n 13.3. Asymptotic Theory of MLEs\n 13.4. A General Form for Regression Models\n 13.5. Nonlinear Regression\n 13.6. Generalized Linear Models (GLM)\n 13.7. Generalized Estimating Equations (GEE)\n 13.8. Existence and Consistency of M-Estimators\n 13.9. Asymptotic Distribution of ˆn\n 13.10. Regularity Conditions for Estimating Equations\n 13.11. Problems\n14. Large Sample Hypothesis Testing\n 14.1. Introduction\n 14.2. Model Assumptions\n 14.3. Large Sample Tests for Simple Null Hypotheses\n 14.4. Nuisance Parameters and Composite Null Hypotheses\n 14.5. Pearson’s ˜x2 Test for Independence in Contingency Tables\n 14.6. A Comparison of the LR, Wald and Score Tests\n 14.7. Confidence Sets\n 14.8. Estimating Power for Approximate ˜x2 Tests\n 14.9. Problems\nA. Parametric Classes of Densities\nB. Topics in Linear Algebra\n B.1. Numbers\n B.2. Equivalence Relations\n B.3. Vector Spaces\n B.4. Matrices\n B.5. Dimension of a Subset of Rd\nC. Topics in Real Analysis and Measure Theory\n C.1. Metric Spaces\n C.2. Measure Theory\n C.3. Integration\n C.4. Exchange of Integration and Differentiation\n C.5. The Gamma and Beta Functions\n C.6. Stirling’s Approximation of the Factorial\n C.7. The Gradient Vector and the Hessian Matrix\n C.8. Normed Vector Spaces\n C.9. Taylor’s Remainder Theorem\nD. Group Theory\n D.1. Definition of a Group\n D.2. Subgroups\n D.3. Group Homomorphisms\n D.4. Transformation Groups\n D.5. Orbits and Maximal Invariants\nBibliography\nIndex