MTH755A - Statistical Inference

Population and samples; Parametric and non parametric models; Exponential and location scale families; Sufficiency and minimal sufficiency; Complete statistics; Unbiased and UMVU estimation; Asymptotically unbiased estimators; Method of moments; Bayes estimators; Invariance; Minimaxity and admissibility; The method of maximum likelihood; Asymptotically efficient estimation; Variance estimation; The jack nife; The bootstrap; The NP lemma; MLR; UMP tests for one and two sided hypotheses; Unbiased and similarity; UMPU tests in exponential families; Invariance and UMPI tests; LR tests; Asymptotic tests based on likely hoods; Chisquare tests; Bayes tests; Pivotal quantities; Inverting acceptance regions of tests; The Bayesian confidence interval; Prediction sets; Length of confidence intervals; UMA and UMAU confidence sets; Invariant confidence sets.