Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions.

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Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions.

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Title: Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions.
Author: Ibragimov, Rustam
Citation: Ibragimov, Rustam. (2007). Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions. Econometric Theory 23(3): 501-517.
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Abstract: This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions. We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of [alpha]-symmetric distributions with [alpha] > 1. However, these properties are reversed in the case of convolutions of [alpha]-symmetric distributions with [alpha] < 1. We show that the sample mean is the best linear unbiased estimator of the population mean for not extremely heavy-tailed populations in the sense of its peakedness. In such a case, the sample mean exhibits monotone consistency, and an increase in the sample size always improves its performance. However, efficiency of the sample mean in the sense of peakedness decreases with the sample size if it is used to estimate the location parameter under extreme heavy-tailedness. We also present applications of the results in the study of concentration inequalities for linear estimators.
Published Version: http://dx.doi.org/10.1017/S0266466607070223
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2623749

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  • FAS Scholarly Articles [6466]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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