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Measure of location-based estimators in simple linear regression
Department of Statistics, Uppsala University, Uppsala, Sweden.
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
Taylor & Francis, 2016. Vol. 86, no 9, 1771-1784 p.
Keyword [en]
simple linear regression, robust estimators, measure of location, stable distribution, contaminated error, finite-sample, exact distribution, special functions
National Category
Probability Theory and Statistics Computer Science
Identifiers
URN: urn:nbn:se:umu:diva-130037DOI: 10.1080/00949655.2015.1082131ISI: 000372035600009OAI: oai:DiVA.org:umu-130037DiVA: diva2:1063931
Available from: 2017-01-11 Created: 2017-01-11 Last updated: 2017-01-11Bibliographically approved

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Liu, XijiaPreve, Daniel
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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf