Advance Statistical Inference

3 Credits · Level: Graduate

This course takes an advanced approach to statistical inference with emphasis on theory and foundations. Topics covered include UMVUE, variance bounds and information inequalities, U-statistics; Bayes decisions and estimators, invariance, MLE, quasi- and conditional likelihoods, and asymptotic relative efficient estimation; empirical likelihoods, density estimation and semi-parametric methods, M-, L-, R-estimation, jackknife and bootstrap; UMP tests, UMP unbiased and similar tests, UMP invariant tests, likelihood ratio tests, asymptotic tests based on the likelihood, Bayes tests, tests in nonparametric models; asymptotic confidence sets, bootstrap confidence sets and simultaneous confidence intervals.