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k-Step shape estimators based on spatial signs and ranks

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Title: k-Step shape estimators based on spatial signs and ranks
Authors: Taskinen, S.1 sara.l.taskinen@maths.jyu.fi, Sirkiä, S.2, Oja, H.3
Source: Journal of Statistical Planning & Inference. Nov2010, Vol. 140 Issue 11, p3376-3388. 13p.
Subjects: Estimation theory, Matrices (Mathematics), Distribution (Probability theory), Analysis of covariance, Statistical research, Least squares, Mathematical statistics
Abstract: Abstract: In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in and and further studied for example in . The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the estimators are derived at the multivariate elliptical case. The estimators are shown to be highly efficient in the multinormal case, and for heavy-tailed distributions they outperform the shape estimator based on sample covariance matrix. [Copyright &y& Elsevier]
Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Abstract: In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in and and further studied for example in . The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the estimators are derived at the multivariate elliptical case. The estimators are shown to be highly efficient in the multinormal case, and for heavy-tailed distributions they outperform the shape estimator based on sample covariance matrix. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Distribution (Probability theory)
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      – SubjectFull: Analysis of covariance
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      – SubjectFull: Statistical research
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      – SubjectFull: Least squares
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      – SubjectFull: Mathematical statistics
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              Text: Nov2010
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