Rank-Based Estimator in Two-Phase Linear Model

• Activity Number: 532
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Brice Merlin Nguelifack*+
• Companies: Auburn University
• Keywords: Two-phase ; Linear ; Model

Abstract

This paper considers two-phase random design linear models with arbitrary error densities and where the regression function has fixed jump at the true change-point. It obtains the consistency, and the limiting distributions of the $R-$estimators of the underlying parameters in these models. The left end point of the minimizing interval with respect to the change point, herein called the $R-$estimator $\hat{r}_n$ of the change-point parameter $r$ is shown to be $n$-consistent and the underlying $R$-process, as a process in the standardized change-point parameter, is shown to converge weakly to a compound poisson process. This process obtains maximum over a bounded interval and $n(\hat{r}_n -r)$ converges weakly to the left end point of this interval. These results are different from those available in the literature for the case of two-phase linear regression models when jump sizes tends to zero as $n$ tends to infinity.