Related papers: Sparse Models and Methods for Optimal Instruments …

In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

In a linear instrumental variables (IV) setting for estimating the causal effects of multiple confounded exposure/treatment variables on an outcome, we investigate the adaptive Lasso method for selecting valid instrumental variables from a…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the "sparsest rule", which is equivalent to the plurality rule but becomes operational in…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…

We study the problem of high-dimensional variable selection via some two-step procedures. First we show that given some good initial estimator which is $\ell_{\infty}$-consistent but not necessarily variable selection consistent, we can…

In this article we study post-model selection estimators that 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 nonparametric…

The endogeneity issue is fundamentally important as many empirical applications may suffer from the omission of explanatory variables, measurement error, or simultaneous causality. Recently, \cite{hllt17} propose a "Deep Instrumental…

A great deal of interest has recently focused on conducting inference on the parameters in a high-dimensional linear model. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso…

For high-dimensional omics data, sparsity-inducing regularization methods such as the Lasso are widely used and often yield strong predictive performance, even in settings when the assumption of sparsity is likely violated. We demonstrate…

This paper is an exposition of how BRIDGE and adaptive LASSO can be used in a two-stage least squares problem, to estimate the second-stage coefficients when the number of parameters p in both stages is growing with the sample size n.…

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear…

Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in {\mathbb R}^p$…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…

This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included…

In many observational studies, researchers are often interested in studying the effects of multiple exposures on a single outcome. Standard approaches for high-dimensional data such as the lasso assume the associations between the exposures…