Parametric Statistical Inference

List of IllustrationsChapter1 General Review 1.1 Introduction 1.2 Statistical Models, Distribution Functions and the Essence of Statistical Inference 1.3 The Information in Samples and Sufficient Statistics 1.4 Testing Statistical Hypotheses 1.5 Estimation Theory 1.6 The Efficiency of Estimators 1.7 Confidence and Tolerance Intervals 1.8 Decision Theoretic and Bayesian Approach in Testing and EstimationChapter 2 Basic Theory of Statistical Distributions 2.1 Introductory Remarks 2.2 Elementary Properties of Distribution Functions 2.2.1 Discrete Distributions 2.2.2 Absolutely Continuous Distributions 2.2.3 Inverse Functions 2.2.4 Transformations 2.3 Some Families of Discrete Distributions 2.3.1 Binomial Distributions 2.3.2 Hypergeometric Distributions 2.3.3 Poisson Distributions 2.3.4 Geometric, Pascal and Negative Binomial 2.4 Some Families of Continuous Distributions 2.4.1 Rectangular Distributions 2.4.2 Beta Distributions 2.4.3 Gamma Distributions 2.4.4 Weibull and Extreme Value Distributions 2.4.5 Normal Distributions 2.4.6 Normal Approximations 2.5 Expectations, Moments and Generating Functions 2.6 Joint Distributions, Conditional Distributions and Independence 2.6.1 Joint Distributions 2.6.2 Conditional Distributions 2.6.3 Independence 2.6.4 Transformations 2.7 Moments and Covariances of Linear Functions 2.8 Discrete Multivariate Distributions 2.8.1 Multinomial Distributions 2.8.2 Multivariate Negative Binomial 2.8.3 Multivariate Hypergeomettic 2.9 Multinormal Distributions 2.9.1 Basic Theory 2.9.2 Distributions of Subvectors and Distributions of Linear Forms 2.9.3 Independence of Linear Forms 2.9.4 Normal Probability Transformations 2.l0 Distributions of Symmetric Quadratic Forms of Normal Variables 2.11 Independence of Linear and Quadratic Forms of Normal Variables 2.l2 The Order Statistics 2.l3 The T-Distributions 2.14 The F-Distributions 2.15 The Distribution of the Sample Correlation 2.16 Limit Theorems 2.17 ProblemsChapter 3 Sufficient Statistics and the Information in Samples 3.1 Introduction 3.2 Definitions and Characterization of Sufficient Statistics 3.3 Likelihood Functions and Minimal Sufficient Statistics 3.4 Sufficient Statistics and Exponential Type Families 3.5 Sufficiency and Completeness 3.6 Information Functions and Sufficiency 3.6.1 The Fisher Information 3.6.2 The Kullback-Leibler Information 3.7 ProblemsChapter 4 Testing Statistical Hypotheses 4.1 The General Framework 4.2 The Neyman-Pearson Fundamental Lemma 4.3 Testing One-Sided Composite Hypotheses in MLR Models 4.4 Testing Two-Sided Hypotheses in One-Parameter Exponential Families 4.5 Testing Composite Hypotheses with Nuisance Parameters-Unbiased Tests 4.6 Likelihood Ratio Tests 4.6.1 Testing in Normal Regression Theory 4.6.2 Comparison of Normal Means: The Analysis of Variance 4.7 The Analysis of Contingency Tables 4.7.1 The Structure of Multi-Way Contingency Tables and the Statistical Model 4.7.2 Testing the Significance of Association 4.7.3 The Analysis of 2x2 Tables 4.7.4 Likelihood Ratio Tests 4.8 Sequential Testing of Hypotheses 4.8.1 The Wa1d Sequential Probability Ratio Test 4.8.2 Sequential Tests with Power 4.9 ProblemsChapter 5 Estimation Theory 5.1 General Discussion 5.2 Unbiased Estimators 5.2.1 General Definition and Example 5.2.2 Minimum Variance Unbiased Estimators 5.2.3 Bias Reduction by Jackknifing 5.3 Best Linear Unbiased and Least Squares Estimator 5.3.1 Best Linear Unbiased Estimators of the Mean 5.3.