On The Nonparametric Function Estimation

Abstract

I will give a summary talk on my past work and to the future perspective. Mainly, I will focus on the wavelet method --the BLUPWAVE sequel, which is a wavelet shrinkage method with Bayesian interpretation and frequentist Gauss- Markov optimality. A data driven GCV for parameters selection and an intensive simulation study are included. Then, I will address briefly the basic idea of the optimal volume-corrected Laplace method, which is a kernel-based correction to the Metropolis-Laplace method for Bayesian marginal probability. Finally, I will also talk a little bit on the nonparametric techniques in the statistical learning theory (particularly, the SVM).