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Measure of location-based estimators in simple linear regression
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
City University of Hong Kong.
2016 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 86, no 9, 1771-1784 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 86, no 9, 1771-1784 p.
Keyword [en]
simple linear regression, robust estimators, measure of location, stable distribution, contaminated error
National Category
Other Natural Sciences
Research subject
URN: urn:nbn:se:uu:diva-222210DOI: 10.1080/00949655.2015.1082131ISI: 000372035600009OAI: diva2:710950
The Jan Wallander and Tom Hedelius Foundation, P 2006-0166:1
Available from: 2014-04-08 Created: 2014-04-08 Last updated: 2016-04-19Bibliographically approved

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