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Asymptotic Properties of Marginal Least-Square Estimator for Ultrahigh-Dimensional Linear Regression Models with Correlated Errors
Authors:Gyuhyeong Goh
Institution:Department of Statistics, Kansas State University, Manhattan, KS
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.
Keywords:Consistency  Correlated errors  Mutual orthogonality  Partial orthogonality  Ultrahigh-dimensionality
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