Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis

Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis

© 2016 by the Mathematical Association of Thailand. All rights reserved. In many practical situations, we do not know the shape of the corresponding probability distributions and therefore, we need to use robust statistical techniques, i.e., techniques that are applicable to all possible distributio...

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Main Authors: Songsak Sriboonchitta, Ildar Batyrshin, Vladik Kreinovich
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008422675&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55981
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-559812018-09-05T03:07:03Z Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis Songsak Sriboonchitta Ildar Batyrshin Vladik Kreinovich Mathematics © 2016 by the Mathematical Association of Thailand. All rights reserved. In many practical situations, we do not know the shape of the corresponding probability distributions and therefore, we need to use robust statistical techniques, i.e., techniques that are applicable to all possible distributions. Empirically, it turns out the the most efficient robust version of sample variance is the average value of the p-th powers of the deviations |xi- â|from the (estimated) mean â. In this paper, we use natural symmetries to provide a theoretical explanation for this empirical success, and to show how this optimal robust version of sample variance can be naturally extended to a robust version of sample covariance. 2018-09-05T03:07:03Z 2018-09-05T03:07:03Z 2016-01-01 Journal 16860209 2-s2.0-85008422675 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008422675&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55981
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Songsak Sriboonchitta
Ildar Batyrshin
Vladik Kreinovich
Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
description © 2016 by the Mathematical Association of Thailand. All rights reserved. In many practical situations, we do not know the shape of the corresponding probability distributions and therefore, we need to use robust statistical techniques, i.e., techniques that are applicable to all possible distributions. Empirically, it turns out the the most efficient robust version of sample variance is the average value of the p-th powers of the deviations |xi- â|from the (estimated) mean â. In this paper, we use natural symmetries to provide a theoretical explanation for this empirical success, and to show how this optimal robust version of sample variance can be naturally extended to a robust version of sample covariance.
format Journal
author Songsak Sriboonchitta
Ildar Batyrshin
Vladik Kreinovich
author_facet Songsak Sriboonchitta
Ildar Batyrshin
Vladik Kreinovich
author_sort Songsak Sriboonchitta
title Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
title_short Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
title_full Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
title_fullStr Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
title_full_unstemmed Which robust versions of sample variance and sample covariance are most appropriate for econometrics: Symmetry-based analysis
title_sort which robust versions of sample variance and sample covariance are most appropriate for econometrics: symmetry-based analysis
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008422675&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55981
_version_ 1681424606683987968

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