We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of...

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 at nearly the oracle rate, and is thus hard to improve...

In the first part of the paper, we consider estimation and inference on policy relevant treatment effects, such as local average and local quantile treatment effects, in a data-rich environment where there may be many more control variables available than there are observations. In addition to...

In this work we consider series estimators for the conditional mean in light of three new ingredients: (i) sharp LLNs for matrices derived from the non-commutative Khinchin inequalities, (ii) bounds on the Lebesgue factor that controls the ratio between the L8 and L2-norms, and (iii) maximal...

We consider estimation of policy relevant treatment effects in a data-rich environ ment where there may be many more control variables available than there are observations. In addition to allowing many control variables, the setting we consider allows heterogeneous treatment effects, endogenous...

In this paper, we consider estimation of general modern moment-condition problems in econometrics in a data-rich environment where there may be many more control variables available than there are observations. The framework we consider allows for a continuum of target parameters and for...

We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of...