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Inference for the Linear IV Model Ridge Estimator Using Training and Test Samples

Author

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  • Fallaw Sowell

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA)

  • Nandana Sengupta

    (School of Public Policy, Indian Institute of Technology Delhi, New Delhi 110016, India)

Abstract

The asymptotic distribution is presented for the linear instrumental variables model estimated with a ridge penalty and a prior where the tuning parameter is selected with a holdout sample. The structural parameters and the tuning parameter are estimated jointly by method of moments. A chi-squared statistic permits confidence regions for the structural parameters. The form of the asymptotic distribution provides insights on the optimal way to perform the split between the training and test sample. Results for the linear regression estimated by ridge regression are presented as a special case.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:43-744:d:628388
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    References listed on IDEAS

    as
    1. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    2. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    3. Hernán Rubio & Luis Firinguetti, 2002. "The Distribution of Stochastic Shrinkage Parameters in Ridge Regression," Working Papers Central Bank of Chile 137, Central Bank of Chile.
    4. Bertille Antoine & Eric Renault, 2009. "Efficient GMM with nearly-weak instruments," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 135-171, January.
    5. 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.
    6. 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.
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