Prof. Fang Li : Asymptotics of the Theil-Sen estimators in a multiple linear regression model when covariates are deterministic

Posted by , part of the Statistics and Data Science Seminar.

At

March 18, 2009, 4 p.m.

In

SEO 612

Abstract

In this talk, we introduce the Multivariate Theil-Sen Estimators (MTSE) in a multiple linear regression model generalizing the TSE in a simple linear model. We demonstrate that the proposed estimators are robust with bounded influence function. We also show that the MTSE is consistent under very mild conditions. When the covariates are independent and identically distributed, the related criterion statistics defining the MTSE are the standard U-statistics. However when the covariates are deterministic, the related criterion statistics are no longer U-statistics. We then use the Convexity Lemma of Pollard to prove its asymptotic normality under mild condition. This method can also be easily generalized to the case when the covariates are independent and identically distributed.