Mathematical Statistics Book

INTRODUCTION TO PROBABILITY Random Experiments Probability Measures Conditional Probability and Independence Random Variables Expected Values RANDOM VECTORS AND JOINT DISTRIBUTIONS Introduction Discrete and Continuous Random Vectors Conditional Distributions Normal Distributions Poisson Processes Generating Random Variables CONVERGENCE OF RANDOM VARIABLES Introduction Convergence in Probability and Distribution WLLN Proving Convergence in Distribution CLT Some Applications Convergence with Probability 1
PRINCIPLES OF POINT ESTIMATION Introduction Statistical Models Sufficiency Point Estimation Substitution Principle Influence Curves Standard Errors Relative Efficiency The Jackknife LIKELIHOOD-BASED ESTIMATION Introduction The Likelihood Function The Likelihood Principle Asymptotics for MLEs Misspecified Models Nonparametric Maximum Likelihood Estimation Numerical Computation Bayesian Estimation OPTIMAL ESTIMATION Decision Theory UMVUEs The Cramér-Rao Lower Bound Asymptotic Efficiency INTERVAL ESTIMATION AND HYPOTHESIS TESTING Confidence Intervals and Regions Highest Posterior Density Regions Hypothesis Testing Likelihood Ratio Tests Other Issues LINEAR AND GENERALIZED LINEAR MODELS Linear Models Estimation Testing Non-Normal Errors Generalized Linear Models Quasi-Likelihood Models GOODNESS OF FIT Introduction Tests Based on the Multinomial Distribution Smooth Goodness of Fit Tests REFERENCES Each chapter also contains a Problems and Complements section