This paper is about the ability and means to root-n consistently and efficiently estimate linear, mean-square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters such as the covariance between two regression...

The paper develops estimation and inference methods for econometric models with partial identification, focusing on models defined by moment inequalities and equalities. Main applications of this framework include analysis of game-theoretic models, regression with missing and mismeasured data,...

Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference...

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...

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances where the number of controls may be much larger than the...

In this article, we review quantile models with endogeneity. We focus on models that achieve indentification through the use of instrumental variables and discuss conditions under which partial and point identification are obtained. We discuss key conditions, which include monotonicity and...