Probability and Statistics Seminar: Efficient estimation of smooth functionals in high and infinite dimensions

Vladimir Koltchinskii, Georgia Tech Title: Efficient estimation of smooth functionals in high and infinite dimensions Abstract: I will discuss a problem of estimation of smooth functionals of parameters of high-dimensional and infinite-dimensional statistical models, representing their nonlinear low-dimensional features. The main goal in these problems is to understand the impact of the smoothness of the functional on the quality of statistical estimation and, in particular, to study the phase transition from slow error rates to faster classical $\sqrt{n}$-rates of the CLT when the smoothness…