Measure of Location-Based Estimators in Simple Linear Regression

Journal of Statistical Computation and Simulation, Vol. 86, 2016.

14 Pages Posted: 25 Aug 2015 Last revised: 11 Jun 2018

See all articles by Xijia Liu

Xijia Liu

University of Umea - Department of Mathematics and Mathematical Statistics

Daniel P. A. Preve

Singapore Management University

Date Written: August 10, 2015

Abstract

In this note we consider certain measure of location-based estimators (MLBEs) for the slope parameter in a linear regression model with a single stochastic regressor. The median-unbiased MLBEs are interesting as they can be robust to heavy-tailed samples and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the MLBEs. In the first case, the regressor and error is assumed to follow a symmetric stable distribution. In the second, other types of regressions, with potentially contaminated errors, are considered. For both cases the consistency and exact finite-sample distributions of the MLBEs are established. Some results for the corresponding limiting distributions are also provided. In addition, we illustrate how our results can be extended to include certain heteroskedastic and multiple regressions. Finite-sample properties of the MLBEs in comparison to the LSE are investigated in a simulation study.

Keywords: simple linear regression, robust estimators, measure of location, stable distribution, contaminated error, finite-sample, exact distribution, special functions

Suggested Citation

Liu, Xijia and Preve, Daniel P. A., Measure of Location-Based Estimators in Simple Linear Regression (August 10, 2015). Journal of Statistical Computation and Simulation, Vol. 86, 2016., Available at SSRN: https://ssrn.com/abstract=2650238

Xijia Liu

University of Umea - Department of Mathematics and Mathematical Statistics ( email )

Samhallsvetarhuset, Plan 2
UmeƄ, SE 901 87
Sweden

Daniel P. A. Preve (Contact Author)

Singapore Management University ( email )

90 Stamford Road
Singapore, 178903
Singapore

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