Mathematical Statistics

Basic information


45 hours


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Statistical Models: Elements of Decision Theory. Bayesian Models. Prediction. Sufficiency. Exponential Models. Methods of Estimation: Minimum contrast estimates. Estimating equations. Weighted least squares. Empirical plug-in estimates. Maximum likelihood. Criteria: Minimax. Bayes. Unbiased. Information Inequality. Robustness. Testing and confidence regions: The Neyman-Pearson Lemma. Uniformly most Powerful Tests. Monotone Likelihood Ratio Models. The Duality between Tests and Confidence Regions. Bayesian Formulations. Likelihood Ratio Procedures. Prediction Intervals. Asymptotic approximations. Consistency. The Delta Method. Asymptotic Normality of Estimates. Asymptotic efficiency of the maximum likelihood estimate.



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