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

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  • Nandana Sengupta

    (School of Public Policy, Indian Institute of Technology Delhi, Delhi 110016, India
    These authors contributed equally to this work.)

  • Fallaw Sowell

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Nandana Sengupta & Fallaw Sowell, 2020. "On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples," Econometrics, MDPI, vol. 8(4), pages 1-25, October.
    • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:4:p:39-:d:422323
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    References listed on IDEAS

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    Cited by:

    1. Fallaw Sowell & Nandana Sengupta, 2021. "Inference for the Linear IV Model Ridge Estimator Using Training and Test Samples," Stats, MDPI, vol. 4(3), pages 1-20, September.

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