Efficiency of linear estimators under heavy-tailedness: Convolutions of α-symmetric distributions
File(s)
Accepted version
Author(s)
Ibragimov, R
Type
Journal Article
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 α-symmetric distributions with α > 1. However, these properties are reversed in the case of convolutions of α-symmetric distributions with α < 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.
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.
Date Issued
2007-06
Date Acceptance
2007-04-01
Citation
Econometric Theory, 2007, 23 (3), pp.501-517
ISSN
0266-4666
Publisher
Cambridge University Press (CUP)
Start Page
501
End Page
517
Journal / Book Title
Econometric Theory
Volume
23
Issue
3
Copyright Statement
© 2007 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Subjects
Social Sciences
Science & Technology
Physical Sciences
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Statistics & Probability
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
CONVEX COMBINATIONS
PEAKEDNESS
1403 Econometrics
Econometrics
Publication Status
Published
Date Publish Online
2007-04-05