In this paper we study post-penalized estimators which apply ordinary, unpenalized linear regression to the model … selected by first-step penalized estimators, typically LASSO. It is well known that LASSO can estimate the regression function … the LASSO-based model selection fails” in the sense of missing some components of the true” regression model. By the true …

We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these … case the ordinary quantile regression is not consistent, we consider quantile regression penalized by the L1-norm of … that applies ordinary quantile regression to the selected model. Fifth, we evaluate the performance of L1-QR in a Monte …

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The …

delta method, and (3) provide results for sparsity-based estimation of regression functions for function-valued outcomes. …

We develop uniformly valid confidence regions for regression coefficients in a highdimensional sparse median regression … of the nuisance part of the median regression function by using Neyman's orthogonalization. We establish that the … resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed …

This work proposes new inference methods for the estimation of a regression coefficient of interest in quantile … regression models. We consider high-dimensional models where the number of regressors potentially exceeds the sample size but a … subset of them suffice to construct a reasonable approximation of the unknown quantile regression function in the model. The …