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Asymptotics for an Adaptive Trimmed Likelihood Location Estimator 

Authors: Tadeusz Bednarski a; Brenton R. Clarke b
Affiliations:   a Institute of Mathematics of the University of Zielona Gova and the Polish Academy of Sciences, Poland.
b Mathematics and Statistics, Division of Science and Engineering, Murdoch University, Murdoch, WA 6150, Australia.
DOI: 10.1080/02331880210933
Publication Frequency: 6 issues per year
Published in: journal Statistics, Volume 36, Issue 1 2002 , pages 1 - 8
Formats available: PDF (English)
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Abstract

An asymptotic normality result is given for an adaptive trimmed likelihood estimator of location, which parallels the asymptotic normality result for the adaptive trimmed mean. The new result comes out of studying the adaptive trimmed likelihood estimator modelled parametrically by a normal family but then examining the behavior when the underlying distribution is in fact some F different from normal. The asymptotic variance of the adaptive estimator is equal to the asymptotic variance of the trimmed likelihood estimator at the optimal trimming proportion for the distribution F, subject to that trimming proportion being positive and F being suitably smooth.
Keywords: Trimmed Likelihood Estimator; Adaptive Estimation
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