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Mathematics  Statistical Inference
Title: Statistical Inference
Department: Mathematics
Author: Prof. Somesh Kumar
University: IIT Kharagpur
Type: WebLink
Abstract: Point Estimation: Parametric point estimation, unbiasedness, consistency, efficiency, method of moments and maximum likelihood, lower bounds for the variance of an estimator, Frechet-Rao-Cramer, Bhattacharya, Chapman-Robbins-Kiefer inequalities. Sufficiency, minimal sufficiency, Factorization Theorem, Rao-Blackwell Theorem, completeness, Lehmann-Scheffe Theorem, UMVUE, Basu’s Theorem, invariance, best equivariant estimators,
Testing of Hypotheses: Tests of hypotheses, simple and composite hypotheses, types of error, Neyman-Pearson Lemma, families with monotone likelihood ratio, UMP, UMP unbiased and UMP invariant tests. Likelihood ratio tests - applications to one sample and two sample problems, Chi-square tests. Wald’s sequential probability ratio test.
Interval estimation: methods for finding confidence intervals, shortest length confidence intervals.
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