University of Arizona 3 credits Mathematics
[Taught Fall semester in even-numbered years] Large sample theory of estimation: modes of convergence, central limit theorems, consistency and asymptotic distribution of estimators,asymptotic relative efficiencies of estimators, autoregressive time series, Cramer-Rao bounds and asymptotic efficiency of the MLE, asymptotic theory of Bayes estimators, semi-parametric linear regression,nonparametric regression and density estimation. Large sample theory of tests: likelihood ratio and Wald's tests in parametric models, the chisquare tests for multinomials, tests for goodness of fit, asymptotic relative efficiencies of tests, nonparametric one- and two-sample tests. Statistical computation: nonparametric bootstrap, Markov Chain Monte Carlo and Bayes theory, hierarchical models.
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