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

Nandana Sengupta,Fallaw Sowell

doi:10.3390/econometrics8040039

Nandana Sengupta, Fallaw Sowell

Open Access

https://doi.org/10.3390/econometrics8040039

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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.

Highlights

This paper concerns the estimation and inference on the structural parameters in the linear instrumental variables (IV) model estimated with ridge regression
On the other hand for the larger sample size of n = 100,000 TSLS estimates produce lower root mean square error (RMSE) values compared to ridge estimates for all three priors
The asymptotic distribution of the ridge estimator when the tuning parameter is selected with a test sample has been characterized

Summary

Introduction

This paper concerns the estimation and inference on the structural parameters in the linear instrumental variables (IV) model estimated with ridge regression. This estimator differs from previous ridge regression estimators in three important areas. The regularization tuning parameter is selected using a randomly selected test sample from the observed data. The empirically selected tuning parameter’s impact on the estimates of the parameters of interest is accounted for by deriving their asymptotic joint distribution, which is a mixture.

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Conclusion