Roussas George G. A Course in Mathematical Statistics

2nd ed. — Academic Press, 1997. — 572 p.A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.Basic Concepts of Set Theory
Some Probabilistic Concepts and Results
On Random Variables and Their Distributions
Distribution Functions, Probability Densities, and Their Relationship
Moments of Random Variables—Some Moment and Probability Inequalities
Characteristic Functions, Moment Generating Functions and Related Theorems
Stochastic Independence with Some Applications
Basic Limit Theorems
Transformations of Random Variables and Random Vectors
Order Statistics and Related Theorems
Sufficiency and Related Theorems
Point Estimation
Testing Hypotheses
Sequential Procedures
Confidence Regions—Tolerance Intervals
The General Linear Hypothesis
Analysis of Variance
The Multivariate Normal Distribution
Quadratic Forms
Nonparametric InferenceAppendix I Topics from Vector and Matrix Algebra
Appendix II Noncentral t-, χ ²-, and F-Distributions
Appendix III Tables
Some Notation and Abbreviations
Answers to Selected Exercises