<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>

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 consider estimation of policy relevant treatment effects in a data-rich environment 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, endeogenous...

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...

In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using ℓ1-penalization and post-ℓ1-penalization methods. Focusing on linear and nonparametric regression frameworks, we discuss various econometric examples, present basic...

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...

In this note, we propose the use of sparse methods (e.g. LASSO, Post-LASSO, p LASSO, and Post-p LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when...

In this work we study 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, such as moment restrictions, on the model, and plays a fundamental role in...

This paper studies the computational complexity of Bayesian and quasi-Bayesian estimation in large samples carried out using a basic Metropolis random walk. The framework covers cases where the underlying likelihood or extremum criterion function is possibly non-concave, discontinuous, and of...

In this paper we study post-model selection estimators which apply ordinary least squares (ols) to the model selected by first-step penalized estimators, typically lasso. It is well known that lasso can estimate the non-parametric regression function at nearly the oracle rate, and is thus hard...