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Stat 410 Syllabus 1-31-10 - Changing variables...

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Statistics 410/Math 464 Course Syllabus Title: Introduction to Mathematical Statistics and Probability II Catalog Description of Course: Same as Mathematics 464. continuation of statistics 400. Includes moment-generating functions, transformations of random variables, normal sampling theory, sufficiency, best estimators, maximum likelihood estimators, method-of-moments estimators, confidence intervals, most powerful tests, unbiased tests, and chi-square tests. Prerequisites: Statistics 400 or both Statistics 100 and Mathematics 461. Credit is not given for both Statistics 410 and 409. Credit: 3 hours or 4 hours. Text: Introduction to Mathematical Statistics, 6th edition, Hogg, McKean and Craig. Pretince Hall. I Distribution of Random Variables: Joint distributions, marginal distributions, conditional distributions, correlation coefficient, bivariate normal distribution II Distributions of Functions of Random Variables:
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Unformatted text preview: Changing variables technique (discrete type, continuous type), order statistics, moment generating function technique, distributions of sample mean and sample variance. III Limiting Distributions: Convergence in distribution and in probability, limiting moment generating functions, Scheffé’s theorem, Slutsky’s theorem, Central Limit Theorem, asymptotic normality, delta method. IV Estimation: Bias, mean square error, consistency, maximum likelihood estimation, method of moments, unbiased estimators, minimum variance unbiased estimators. V Statistical Hypotheses: Best test for simple hypotheses: Neyman-Pearson Lemma, uniformly most powerful tests, likelihood ratio tests. VI Sufficient Statistics: Rao-Blackwell theorem, completeness and uniqueness, exponential family of densities, case of several parameters, Rao-Cramer inequality....
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