Measure of location-based estimators in simple linear regression

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Original languageEnglish
Pages (from-to)1771-1784
Journal / PublicationJournal of Statistical Computation and Simulation
Issue number9
Online published10 Sept 2015
Publication statusPublished - 2016


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.

Research Area(s)

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