COURSE NUMBER AND TITLE: MATH 5220 Estimation and Hypothesis Testing
CREDIT HOURS: 3
CATALOG DESCRIPTION: Introduction to the theoretical properties of point estimators and tests of hypotheses, sufficient statistics, likelihood, best linear unbiased estimates, elements of statistical tests, the Neyman Pearson Lemma, UMP tests, univariate normal inference, decision theory and multivariate distributions are covered.
PREREQUISITE(S): MATH 4251 (grade of C or better) and MATH 5110 (grade of C or better)
SUGGESTED TEXT(S): Probability and Statistics, by Degroot and Schervish, Third Edition, Addison Wesley, 2002.
Special Distributions – Multinomial and bivariate normal distribution.
Estimation – Prior, posterior and conjugate prior distributions, Bayes and Maximum likelihood estimators and their properties, sufficient and jointly sufficient statistics.
Sampling Distributions of Estimators – Chi-square and t-distributions, confidence intervals, Bayesian analysis of samples from normal distribution, unbiased estimators, Fisher information.
Testing of Hypothesis – F-distribution, Testing of hypotheses about one and two population parameters, uniformly most powerful tests, Bayes test procedures.
Categorical Data and Nonparametric Methods – Test of goodness- of- fit, contingency tables, test of homogeneity, Kolmogorov –Smirnov tests, robust estimation, sign and rank tests.