# Inference for High-Dimensional Sparse Econometric Models

@article{Belloni2011InferenceFH, title={Inference for High-Dimensional Sparse Econometric Models}, author={Alexandre Belloni and Victor Chernozhukov and Christian Hansen}, journal={arXiv: Methodology}, year={2011}, pages={245-295} }

Introduction We consider linear, high-dimensional sparse (HDS) regression models in econometrics. The HDS regression model allows for a large number of regressors, p , which is possibly much larger than the sample size, n , but imposes that the model is sparse. That is, we assume that only s ≪ n of these regressors are important for capturing the main features of the regression function. This assumption makes it possible to effectively estimate HDS models by searching for approximately the…

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## References

SHOWING 1-10 OF 52 REFERENCES

### High Dimensional Sparse Econometric Models : An

- Economics
- 2011

In this chapter we discuss conceptually high dimensional sp rse econometric models as well as estimation of these models using l1-penalization and postl1-penalization methods. Focusing on linear and…

### L1-Penalized Quantile Regression in High Dimensional Sparse Models

- Mathematics, Computer Science
- 2009

This work proposes a pivotal, data-driven choice of the regularization parameter and shows that it satisfies certain theoretical constraints and evaluates the performance of L1-QR in a Monte-Carlo experiment, and provides an application to the analysis of the international economic growth.

### High-dimensional instrumental variables regression and confidence sets

- Economics, Mathematics
- 2011

We propose an instrumental variables method for inference in high-dimensional structural equations with endogenous regressors. The number of regressors K can be much larger than the sample size. A…

### Group Lasso for high dimensional sparse quantile regression models

- Computer Science, Mathematics
- 2011

A non-asymptotic bound on the $\ell_{2}$-estimation error of the estimator is established and it is shown that under a set of suitable regularity conditions, the group Lasso estimator can attain the convergence rate arbitrarily close to the oracle rate.

### Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models

- Mathematics, Economics
- 2007

### Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain

- Economics, Mathematics
- 2010

A fully data-driven method for choosing the user-specified penalty that must be provided in obtaining LASSO and Post-LASSO estimates is provided and its asymptotic validity under non-Gaussian, heteroscedastic disturbances is established.

### Asymptotic properties of bridge estimators in sparse high-dimensional regression models

- Mathematics
- 2008

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are…

### Estimation with Weak Instruments: Accuracy of Higher-Order Bias and MSE Approximations

- Mathematics, Economics
- 2004

In this paper, we consider parameter estimation in a linear simultaneous equations model. It is well known that two-stage least squares (2SLS) estimators may perform poorly when the instruments are…

### Instrumental Variables Regression with Weak Instruments

- Economics, Mathematics
- 1994

This paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak, here…

### Quantile Regression Under Misspecification, with an Application to the U.S. Wage Structure

- Mathematics
- 2004

Quantile regression(QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives…