11/18/2017

Post date: Nov 21, 2017 6:12:37 PM

Title: Adaptive Estimation of High Dimensional Partially Linear Model

Speaker: Fang Han, Department of Statistics, University of WashingtonDepartment of Statistics

Abstract: Consider the partially linear model (PLM) with random design: Y=X\beta^*+g(W)+u, where g(.) is an unknown real-valued function, X is p-dimensional, W is one-dimensional, and \beta^* is s-sparse. Our aim is to estimate \beta^* based on n i.i.d. observations of (Y,X,W) with possibly n<p. The popular approaches and their theoretical properties so far have mainly been developed with an explicit knowledge of some function classes. In this talk, I will present an adaptive estimation procedure, with consistency and exact rates of convergence obtained in high dimensions under mild scaling requirements. Two surprising features are revealed: (i) the bandwidth parameter automatically adapts to the model and is actually tuning-insensitive; and (ii) the procedure could even maintain fast rate of convergence for \alpha-Holder class of \alpha<1/2.