Official Course Description
Weak convergence on general function spaces. Nonmeasurable functionals (Hoffman-Jörgensen's theory). Characterization of tightness and convergence of finite dimensional distributions. Empirical processes. Covering numbers and bracketing numbers. VC classes of functions. Functional differentiability (smooth statistical functionals). Application to survival analysis (Nelson-Aalen and Kaplan-Meier estimators). Quantile estimators. Bootstrap methods, functional differentiability for bootstrap, bootstrap for empirical processes. Nonparametric estimation of densities. Limit distributions. Convergence rates. The partial sum process. Donsker's theorem for this. Nonparametric estimations of regression functions. M and Z estimators. Applications to maximum likelihood och least square estimators. Empirical processes and partial sum process results for weakly and strongly dependent stationary data. Kernel estimation of densities and regression functions. The empirical spectral process. Nonparametric estimation of spectral densities.