We develop uniformly valid confidence regions for a regression coefficient in a high-dimensional sparse LAD (least absolute deviation or median) regression model. The setting is one where the number of regressors p could be large in comparison to the sample size n, but only s « n of them are...

We propose a self-tuning √ Lasso method that simultaneiously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity, and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly...

We develop uniformly valid conï¬dence regions for regression coefficients in a high-dimensional sparse least absolute deviation/median regression model. The setting is one where the number of regressors p could be large in comparison to the sample size n, but only s ≪ n of them are...

This paper considers inference in logistic regression models with high dimensional data. We propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest ?0 a parameter in front of the regressor of interest, such as the treatment variable...

<p><p>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...</p></p>

<p>In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states...</p>

<p><p>We develop results for the use of LASSO and Post-LASSO methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n. We rigorously develop asymptotic...</p></p>

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...

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...

The goal of many empirical papers in economics is to provide an estimate of the causal or structural effect of a change in a treatment or policy variable, such as a government intervention or a price, on another economically interesting variable, such as unemployment or amount of a product...