|
Activity Number:
|
33
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Sunday, August 6, 2006 : 2:00 PM to 3:50 PM
|
|
Sponsor:
|
Section on Nonparametric Statistics
|
| Abstract - #307437 |
|
Title:
|
Multivariate Theil-Sen Estimators
|
|
Author(s):
|
Xin Dang*+ and Hanxiang Peng and Xueqin Wang
|
|
Companies:
|
University of Mississippi and University of Mississippi and Yale University School of Medicine
|
|
Address:
|
Department of Mathematics, University, MS, 38677,
|
|
Keywords:
|
strong consistency ; asymptotic normality ; nonparametric statistics ; multivariate linear regression
|
|
Abstract:
|
As an alternative of Least square estimator (LSE), the Theil-Sen estimator was introduced in a simple linear regression model, which is robust to the outliers and easy to be interpreted in a geometric view. However, the generalization of this estimator to multivariate linear regression have not gained enough attention because of technical difficulty. With the recent development of the depth function which is a method to describe the center of data in the high-dimension space. We use varied depth functions to construct the Theil-Sen estimators for multivariate linear regression model. The strong consistency and the asymptotic behaviors are investigated under modest conditions. The asymptotic relative efficiencies (A.R.E.) and the robustness properties are also compared for different depth functions. simulations are performed to verify the properties of estimators.
|
