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Statistical Inference

(Stat 559)


Point Estimation: Properties of estimator: sufficiency, Neyman-Fisher's criteria for sufficiency, Minimal sufficiency, Exponential family, unbiasedness, uniformly minimum variance unbiased estimator, Cramer-Rao inequality and it's generalization, Fisher's information, Rao-Blackwell theorem, sufficiency and completeness, Lehmann-Sheffe theorem, Robust estimators, Estimation from truncated and censored distribution. The Baysian Approach: Use of prior density, Bayes estimators,  Bayes estimators with mean square error, loss function, Admissibility. Minimax estimator. Other classes of estimators: Location invariant and scale invariant classes of estimators. Interval estimation: Confidence interval estimators, Pivotal methods, Baysian interval estimators and Fiducial interval estimators, central and non-central confidence interval. Methods of Estimation: Maximum Likelihood estimators and their properties including asymptotic properties, practical consideration in solving maximum likelihood equations and other methods. Hypotheses Testing: Most powerful test, Neymann-peasson lemma, asymptotic efficiency of a test, unbiased and similar test, UMP, UMPU and LUMPU test, similar regions, Neymann theorem, power curves, Likelihood ratio tests, asymptotes distribution of likelihood ratio statistics. Test of independence in multi-way contingency table.





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