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...

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 paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to...

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...

This article looks at the theory and empirics of extremal quantiles in economics, in particular value-at-risk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings in the last 20 years. In the discussion, we put a particular focus on...

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved...

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of...