High-Dimensional Instrumental Variables Regression and Confidence Sets
AbstractWe propose an instrumental variables method for estimation in linear models with endogenous regressors in the high-dimensional setting where the sample size n can be smaller than the number of possible regressors K, and L>=K instruments. We allow for heteroscedasticity and we do not need a prior knowledge of variances of the errors. We suggest a new procedure called the STIV (Self Tuning Instrumental Variables) estimator, which is realized as a solution of a conic optimization program. The main results of the paper are upper bounds on the estimation error of the vector of coefficients in l_p-norms for 1
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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2011-13.
Date of creation: May 2011
Date of revision:
Instrumental Variables; Sparsity; STIV Estimator; Endogeneity; High-Dimensional Regression; Conic Programming; Optimal Instruments; Hereroscedasticity; Confidence Intervals; Non-Gaussian Errors; Variable Selection; Unknown Variance; Sign Consistency;
Other versions of this item:
- Eric Gautier & Alexandre Tsybakov, 2011. "High-dimensional instrumental variables regression and confidence sets," Working Papers hal-00591732, HAL.
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