3.0

credits

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This course is a continuation of 626.725. The course further deepens your understanding of mathematical foundations of statistical methods through an analysis of standard and contemporary methods. This course starts with decision theory, and then continues with density estimation, nonparametric regression methods (kernels, local polynomials), nonparametric classification (density based, kernels, trees), high dimensional methods (lasso, ridge regression), statistical analysis of graphical models, minimax theory, causality, dimensionality reduction, mixture models, boosting, conformal methods, M-estimation, U-statistics, empirical processes and semiparametric models, use of concentration inequalities, bias and variance, the central limit theorem, likelihood and sufficiency, point estimation (MLE, method of moments and Bayes), asymptotic theory, confidence intervals, bootstrap methods, high dimensional statistics, and model selection.