Asymptotic Properties of Marginal Least-Square Estimator for Ultrahigh-Dimensional Linear Regression Models with Correlated Errors

Gyuhyeong Goh and Dipak K. Dey

The American Statistician, 2019, vol. 73, issue 1, 4-9

Abstract: In this article, we discuss asymptotic properties of marginal least-square estimator for ultrahigh-dimensional linear regression models. We are specifically interested in probabilistic consistency of the marginal least-square estimator in the presence of correlated errors. We show that under a partial orthogonality condition, the marginal least-square estimator can achieve variable selection consistency. In addition, we demonstrate that if a mutual orthogonality holds, the marginal least-square estimator satisfies estimation consistency. The discussed theories are exemplified through extensive simulation studies.

Date: 2019
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DOI: 10.1080/00031305.2017.1302359

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