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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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