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Open AccessArticle

On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples

by Nandana Sengupta 1,† and Fallaw Sowell 2,*,†
1
School of Public Policy, Indian Institute of Technology Delhi, Delhi 110016, India
2
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Econometrics 2020, 8(4), 39; https://doi.org/10.3390/econometrics8040039
Received: 25 November 2019 / Revised: 10 September 2020 / Accepted: 11 September 2020 / Published: 1 October 2020
The asymptotic distribution of the linear instrumental variables (IV) estimator with empirically selected ridge regression penalty is characterized. The regularization tuning parameter is selected by splitting the observed data into training and test samples and becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares. An empirical application on returns to education data is presented. View Full-Text
Keywords: ridge regression; instrumental variables; regularization; training and test samples; generalized method of moments framework ridge regression; instrumental variables; regularization; training and test samples; generalized method of moments framework
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Sengupta, N.; Sowell, F. On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples. Econometrics 2020, 8, 39.

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