Mathematical Statistics: Basic Ideas and Selected Topics

摘要: (NOTE: Each chapter concludes with Problems and Complements, Notes, References.) 1. Statistical Models, Goals, Performance Criteria. Data, Parameters, Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families. 2. Methods of Estimation. Basic Heuristics Minimum Contrast Estimates Estimating Equations. Maximum Likelihood in Multiparameter Algorithmic Issues. 3. Measures Performance. Introduction. Bayes Procedures. Minimax Unbiased Estimation Risk Inequalities. Nondecision 4. Testing Confidence Regions. Choosing a Test Statistic: Neyman-Pearson Lemma. Uniformly Most Powerful Tests Monotone Ratio Bounds, Intervals Duality between Regions Tests. Accurate Bounds. Frequentist Formulations. Prediction Intervals. 5. Asymptotic Approximations. Introduction: Meaning Uses Asymptotics. Consistency. First- Higher-Order Asymptotics: Delta Method Applications. Theory One Dimension. Behavior Optimality the Posterior Distribution. 6. Inference Case. for Gaussian Linear p Dimensions. Large Sample Discrete Data. Generalized Robustness Properties Semiparametric Appendix A: A Review Probability Theory. Model. Elementary Conditional Independence. Compound Experiments. Bernoulli Multinomial Trials, Sampling without Replacement. Probabilities on Euclidean Space. Random Variables Vectors: Transformations. Independence Vectors. Expectation Variable. Moments. Moment Cumulant Generating Functions. Some Classical Continuous Distributions. Modes Convergence Limit Theorems. Further Theorems Poisson Process. B: Additional Topics Analysis. Conditioning by Variable or Vector. Distribution Transformations Samples from Normal Population. Bivariate Moments Vectors Matrices. Multivariate Op Notation. Calculus. Convexity Matrix Hilbert Space C: Tables. Standard Auxiliary Table t Critical Values. X 2 F Index.