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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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    1. Peter Bickel & Bo Li & Alexandre Tsybakov & Sara Geer & Bin Yu & Teófilo Valdés & Carlos Rivero & Jianqing Fan & Aad Vaart, 2006. "Regularization in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 271-344, September.
    2. Sanderson, Eleanor & Windmeijer, Frank, 2016. "A weak instrument F-test in linear IV models with multiple endogenous variables," Journal of Econometrics, Elsevier, vol. 190(2), pages 212-221.
    3. Marine Carrasco & Guy Tchuente, 2016. "Efficient Estimation with Many Weak Instruments Using Regularization Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1609-1637, December.
    4. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    5. Zhu, Ying, 2018. "Sparse linear models and l1-regularized 2SLS with high-dimensional endogenous regressors and instruments," Journal of Econometrics, Elsevier, vol. 202(2), pages 196-213.
    6. Wei Lin & Rui Feng & Hongzhe Li, 2015. "Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 270-288, March.
    7. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    8. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    10. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    11. Luis Firinguetti & Gladys Bobadilla, 2011. "Asymptotic confidence intervals in ridge regression based on the Edgeworth expansion," Statistical Papers, Springer, vol. 52(2), pages 287-307, May.
    12. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    13. Ali Habibnia & Esfandiar Maasoumi, 2021. "Forecasting in Big Data Environments: An Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 363-381, December.
    14. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    15. Andrews, Donald W K, 2002. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 530-544, October.
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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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