Mathematical Statistics (Hardcover)

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 Cramer-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