The distribution of test statistics for outlier detection in heavy-tailed samples

S. Mittnik; S. T. Rachev; G. Samorodnitsky

doi:10.1016/S0895-7177(01)00125-X

The distribution of test statistics for outlier detection in heavy-tailed samples

S. Mittnik, S. T. Rachev, G. Samorodnitsky

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n^-1/2O_n for the outlier statistic when the observations X_i are the domain of attraction of an α-stable law. We present approximate critical values for O_n for finite samples using response surface methods.

Original language	English
Pages (from-to)	1171-1183
Number of pages	13
Journal	Mathematical and Computer Modelling
Volume	34
Issue number	9-11
DOIs	https://doi.org/10.1016/S0895-7177(01)00125-X
State	Published - Sep 24 2001

Keywords

Financial modeling
Infinite variance
Risk management
Robust statistics

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10.1016/S0895-7177(01)00125-X

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title = "The distribution of test statistics for outlier detection in heavy-tailed samples",

abstract = "We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n-1/2On for the outlier statistic when the observations Xi are the domain of attraction of an α-stable law. We present approximate critical values for On for finite samples using response surface methods.",

keywords = "Financial modeling, Infinite variance, Risk management, Robust statistics",

author = "S. Mittnik and Rachev, {S. T.} and G. Samorodnitsky",

note = "Funding Information: Parts of the work were conducted whiic Kachcv visited the, lilliversily of Kiel with support from the Alexander-von-Humboldt Foundation. The research of .\littnik was supportc%ti by the Deutsche Forschullgsgemeinschaft (DFG) and that of Samorodnitsky by h{\textquoteright}SF Grant,s DhIS-97-04982 and DMI-97-13549 alld by the NSA Grant MDA904-98-l-0041 at Cornell University.",

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doi = "10.1016/S0895-7177(01)00125-X",

language = "English",

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T1 - The distribution of test statistics for outlier detection in heavy-tailed samples

AU - Mittnik, S.

AU - Rachev, S. T.

AU - Samorodnitsky, G.

N1 - Funding Information: Parts of the work were conducted whiic Kachcv visited the, lilliversily of Kiel with support from the Alexander-von-Humboldt Foundation. The research of .\littnik was supportc%ti by the Deutsche Forschullgsgemeinschaft (DFG) and that of Samorodnitsky by h’SF Grant,s DhIS-97-04982 and DMI-97-13549 alld by the NSA Grant MDA904-98-l-0041 at Cornell University.

PY - 2001/9/24

Y1 - 2001/9/24

N2 - We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n-1/2On for the outlier statistic when the observations Xi are the domain of attraction of an α-stable law. We present approximate critical values for On for finite samples using response surface methods.

AB - We investigate the asymptotic behavior of outliers test samples statistics for drawn from heavy-tailed distributions. We extend classical results of David et al. [1] and Grubbs [2], who considered outlier test statistics for the finite-variance case, to the heavy-tailed infinite variance case. Our main result concerns the limiting distribution of n-1/2On for the outlier statistic when the observations Xi are the domain of attraction of an α-stable law. We present approximate critical values for On for finite samples using response surface methods.

KW - Financial modeling

KW - Infinite variance

KW - Risk management

KW - Robust statistics

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U2 - 10.1016/S0895-7177(01)00125-X

DO - 10.1016/S0895-7177(01)00125-X

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VL - 34

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EP - 1183

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

IS - 9-11

ER -

The distribution of test statistics for outlier detection in heavy-tailed samples

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Keywords

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