Prof. Runze Li : Penalized Quantile Regression for Ultra-high Dimensional Data

Posted by Min Yang , part of the Statistics and Data Science Seminar.

At

Dec. 5, 2012, 4 p.m.

In

SEO 636

Abstract

Ultra-high dimensional data often display heterogeneity due to either heteroscedastic variance or other forms of non-location-scale covariate effects. To accommodate heterogeneity, we advocate a more general interpretation of sparsity which assumes that only a small number of covariates influence the conditional distribution of the response variable given all candidate covariates; however, the sets of relevant covariates may differ when we consider different segments of the conditional distribution. In this talk, I first introduce recent development on the methodology and theory of nonconvex penalized quantile linear regression in ultra-high dimension. I further propose a two-stage feature screening and cleaning procedure to study the estimation of the index parameter in heteroscedastic single-index models with ultrahigh dimensional covariates. Sampling properties of the proposed procedures are studied. Finite sample performance of the proposed procedure is examined by Monte Carlo simulation studies. A real example example is used to illustrate the proposed methodology.