I. Number and Title of course

MATH 683 - Statistical Theory

A. To provide a graduate level course in Mathematical statistics.

B. To provide for these students who have had a one semester introduction to Mathematical probability at the undergraduate level, an opportunity to acquaint themselves with statistical theory and its application.

A. To introduce the student to the basic statistical theory used for the analytical assessment of sampled data and to the fundamental statistical techniques employed by researchers in the published literature of this area.

B. To develop mathematical models for the study of random data.

C. To produce computational methods and formulas appropriate to the evaluation and interpretation of experimental data.

The topics A through E below comprise the nucleus of this course. As time permits, the instructor can select from the topics F, G and H for inclusion of additional material in this course.

A. Probability
B. population and samples

1. The Chi-square, t and F distributions

C. Estimation

1. Methods of moments and maximum Likelihood.
2. Properties of Estimators

D. Confidence Sets

1. Common Confidence Intervals
2. A general method for obtaining confidence sets

E. Tests of Hypotheses

1. Simple hypotheses
2. Composite Hypotheses
3. Sequential tests

F. Decision Theory and Bayesian Methods

1. Bayesian estimation
2. Intervals and tests

G. Linear Models

1. Least squares estimation
2. Experimental design models

H. Nonparametric Methods

1. Order statistics and permutations
2. Nonparametric procedures.