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Efficiency comparison of M-estimates for scale at t-distributions

Efficiency comparison of M-estimates for scale at t-distributions Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated and graphically illustrated. The compared estimators are the standard deviationS *, the mean absolute deviation, called mean deviationD *, the median absolute deviation, called MAD*, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending χ-function too. Also the $$ \hat \sigma _* $$ , an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale estimator $$ \hat \sigma _* $$ in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of $$ \hat \sigma _* $$ is, the lower is the corresponding $$ \hat \sigma _* $$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Papers Springer Journals

Efficiency comparison of M-estimates for scale at t-distributions

Statistical Papers , Volume 41 (1) – Jul 2, 2008

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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag
Subject
Statistics; Statistics for Business/Economics/Mathematical Finance/Insurance; Probability Theory and Stochastic Processes; Economic Theory; Operations Research/Decision Theory
ISSN
0932-5026
eISSN
1613-9798
DOI
10.1007/BF02925676
Publisher site
See Article on Publisher Site

Abstract

Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated and graphically illustrated. The compared estimators are the standard deviationS *, the mean absolute deviation, called mean deviationD *, the median absolute deviation, called MAD*, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending χ-function too. Also the $$ \hat \sigma _* $$ , an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale estimator $$ \hat \sigma _* $$ in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of $$ \hat \sigma _* $$ is, the lower is the corresponding $$ \hat \sigma _* $$ .

Journal

Statistical PapersSpringer Journals

Published: Jul 2, 2008

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