This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. There is a variety of economic applications where solving this problem allows to carry out inference on causal and...

In this paper, we derive new, nearly optimal bounds for the Gaussian approximation to scaled averages of n independent high-dimensional centered random vectors X1, . . . , Xn over the class of rectangles in the case when the covariance matrix of the scaled average is non-degenerate. In the case...

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special...

This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size. We first present results in...

We develop two new methods for selecting the penalty parameter for the e1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-after-cross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding e1-penalized M-estimator...

We consider inference about coefficients on a small number of variables of interest in a linear panel data model with additive unobserved individual and time specific effects and a large number of additional time-varying confounding variables. We allow the number of these additional confounding...