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

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

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

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

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

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

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

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

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

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

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
...