CA252 - Mathematical Statistics II

Estimation

Different approaches to estimation : method of moments, Least Squares, Best Linear Unbiased, Maximum Likelihood and         criteria for optimal estimates : unbiasedness, efficiency, consistency.

Ordinary Least Squares for the General Linear Model and examples : simple regression, dummy variables, ANOVA, transforming non-linear relationships to linear relationships.

Distribution of the OLS parameter vector estimate and the residual vector. Distribution of s².
t-statistics for OLS parameters. F test. R squared.

Best Linear Unbiased Estimates in the General Linear Model and the Gauss-Markov Theorem.

Maximum Likelihood Estimation with examples. Derivation of the Cramer-Rao Bound. Examples of the CR bound.

Hypothesis Testing

Best Tests. The Neyman-Pearson Lemma and applications to various tests..
Likelihood Ratio Tests with examples (including Chi-Square Goodness of fit test).
Introduction to Non-Parametric Methods.
Chebychev's Inequality.

Textbooks

Hoel, Paul, Introduction to Mathematical Statistics, Wiley. 1984

Hogg, R. V. & Craig, A. T. Introduction to Mathematical Statistics, MacMillan, 1978

A recent (Jan 2006) text I found good (and ordered 3 copies for library) is

Wackerly, Denis D., Mendenhall, William III and Scheaffer, Richard L., Mathematical Statistics with Applications, 2002, Duxbury.