We propose both a penalized quantile regression and an independence screening procedure to identify important covariates and to exclude unimportant ones for a general class of ultrahigh dimensional single-index models, in which the conditional distribution of the response depends on the covariates via a single-index structure. We observe that the linear quantile regression yields a consistent e...

Differential gene expression detection and sample classification using microarray data have received much research interest recently. Owing to the large number of genes p and small number of samples n (p >> n), microarray data analysis poses big challenges for statistical analysis. An obvious problem owing to the 'large p small n' is over-fitting. Just by chance, we are likely to find some non-...

Lq-penalized regression arises in multidimensional statistical modelling where all or part of the regression coefficients are penalized to achieve both accuracy and parsimony of statistical models. There is often substantial computational difficulty except for the quadratic penalty case. The difficulty is partly due to the nonsmoothness of the objective function inherited from the use of the ab...

In this paper we study post-penalized estimators which apply ordinary, unpenal-ized linear regression to the model selected by first-step penalized estimators, typically LASSO.