142,251 research outputs found
Inference for High-Dimensional Sparse Econometric Models
This article is about estimation and inference methods for high dimensional
sparse (HDS) regression models in econometrics. High dimensional sparse models
arise in situations where many regressors (or series terms) are available and
the regression function is well-approximated by a parsimonious, yet unknown set
of regressors. The latter condition makes it possible to estimate the entire
regression function effectively by searching for approximately the right set of
regressors. We discuss methods for identifying this set of regressors and
estimating their coefficients based on -penalization and describe key
theoretical results. In order to capture realistic practical situations, we
expressly allow for imperfect selection of regressors and study the impact of
this imperfect selection on estimation and inference results. We focus the main
part of the article on the use of HDS models and methods in the instrumental
variables model and the partially linear model. We present a set of novel
inference results for these models and illustrate their use with applications
to returns to schooling and growth regression
A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models
Inference for spatial generalized linear mixed models (SGLMMs) for
high-dimensional non-Gaussian spatial data is computationally intensive. The
computational challenge is due to the high-dimensional random effects and
because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be
slow mixing. Moreover, spatial confounding inflates the variance of fixed
effect (regression coefficient) estimates. Our approach addresses both the
computational and confounding issues by replacing the high-dimensional spatial
random effects with a reduced-dimensional representation based on random
projections. Standard MCMC algorithms mix well and the reduced-dimensional
setting speeds up computations per iteration. We show, via simulated examples,
that Bayesian inference for this reduced-dimensional approach works well both
in terms of inference as well as prediction, our methods also compare favorably
to existing "reduced-rank" approaches. We also apply our methods to two real
world data examples, one on bird count data and the other classifying rock
types
Private Estimation and Inference in High-Dimensional Regression with FDR Control
This paper presents novel methodologies for conducting practical
differentially private (DP) estimation and inference in high-dimensional linear
regression. We start by proposing a differentially private Bayesian Information
Criterion (BIC) for selecting the unknown sparsity parameter in DP-Lasso,
eliminating the need for prior knowledge of model sparsity, a requisite in the
existing literature. Then we propose a differentially private debiased LASSO
algorithm that enables privacy-preserving inference on regression parameters.
Our proposed method enables accurate and private inference on the regression
parameters by leveraging the inherent sparsity of high-dimensional linear
regression models. Additionally, we address the issue of multiple testing in
high-dimensional linear regression by introducing a differentially private
multiple testing procedure that controls the false discovery rate (FDR). This
allows for accurate and privacy-preserving identification of significant
predictors in the regression model. Through extensive simulations and real data
analysis, we demonstrate the efficacy of our proposed methods in conducting
inference for high-dimensional linear models while safeguarding privacy and
controlling the FDR
Inference for high-dimensional sparse econometric models
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of regressors. We discuss methods for identifying this set of regressors and estimating their coefficients based on l1 -penalization and describe key theoretical results. In order to capture realistic practical situations, we expressly allow for imperfect selection of regressors and study the impact of this imperfect selection on estimation and inference results. We focus the main part of the article on the use of HDS models and methods in the instrumental variables model and the partially linear model. We present a set of novel inference results for these models and illustrate their use with applications to returns to schooling and growth regression.
High-dimensional regression adjustments in randomized experiments
We study the problem of treatment effect estimation in randomized experiments
with high-dimensional covariate information, and show that essentially any
risk-consistent regression adjustment can be used to obtain efficient estimates
of the average treatment effect. Our results considerably extend the range of
settings where high-dimensional regression adjustments are guaranteed to
provide valid inference about the population average treatment effect. We then
propose cross-estimation, a simple method for obtaining finite-sample-unbiased
treatment effect estimates that leverages high-dimensional regression
adjustments. Our method can be used when the regression model is estimated
using the lasso, the elastic net, subset selection, etc. Finally, we extend our
analysis to allow for adaptive specification search via cross-validation, and
flexible non-parametric regression adjustments with machine learning methods
such as random forests or neural networks.Comment: To appear in the Proceedings of the National Academy of Sciences. The
present draft does not reflect final copyediting by the PNAS staf
- …