Mathematical Statistics: Nonparametric Inference

<p>An advanced course in non-parametric statistics that gives solid theoretical foundation.</p><p>Weak convergence on general function spaces. Non-measurable functionals (Hoffman-Jörgensen's theory). Characterization of tightness and convergence of finite dimensional distributions.</p> <p>Empirical processes. Covering numbers and bracketing numbers. VC-classes of functions.</p> <p>Functional differentiability  (smooth statistical functionals). Application to survival analysis  (Nelson-Aalen and Kaplan-Meier estimators).</p> <p>Quantile estimators.</p> <p>Bootstrap methods,  functional differentiability for bootstrap, bootstrap for empirical processes.</p> <p>Nonparametric estimation of densities. Limit distributions. Convergence rates.</p> <p>The partial sum process. Donsker's theorem for this. Nonparametric estimations of regression functions.</p> <p>M and Z estimators. Applications to maximum likelihood och least square estimators.</p> <p>Empirical processes and partial sum process results for weakly and strongly dependent stationary data. Kernel estimation of densities and regression functions.</p> <p>The empirical spectral process. Nonparametric estimation of spectral densities.</p>