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...

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 develop uniformly valid confidence 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 needed to accurately describe the regression function. Our new methods are based on the instrumental median regression estimator that assembles the optimal estimating equation from the output of the post l1-penalized median regression and post l1-penalized least squares in an auxiliary equation. The estimating equation is immunized against non-regular estimation of nuisance part of the median regression function, in the sense of Neyman. We establish that in a homoscedastic regression model, the instrumental median regression estimator of a single regression coefficient is asymptotically root-n normal uniformly with respect to the underlying sparse model. The resulting confidence regions are valid uniformly with respect to the underlying model. We illustrate the value of uniformity with Monte-Carlo experiments which demonstrate that standard/naive post-selection inference breaks down over large parts of the parameter space, and the proposed method does not. We then generalize our method to the case where p1 > n regression coefficients...</<>

This work studies the large sample properties of the posteriorbased inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in...

We propose a self-tuning Í 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...

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...

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...

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...

This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in...