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: NeymanPearson Lemma, uniformly most powerful tests, likelihood ratio tests. VI Sufficient Statistics: RaoBlackwell theorem, completeness and uniqueness, exponential family of densities, case of several parameters, RaoCramer inequality....
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This note was uploaded on 06/11/2010 for the course STAT 410 taught by Professor Alexeistepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 AlexeiStepanov
 Statistics, Probability

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