Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

Søren Johansen; Bent Nielsen

doi:10.1111/sjos.12174

Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models

31 Citations (Scopus)

Abstract

Outlier detection algorithms are intimately connected with robust statistics that down-weight some observations to zero. We define a number of outlier detection algorithms related to the Huber-skip and least trimmed squares estimators, including the one-step Huber-skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.

Original language	English
Journal	Scandinavian Journal of Statistics
Volume	43
Issue number	2
Pages (from-to)	321-348
Number of pages	28
ISSN	0303-6898
DOIs	https://doi.org/10.1111/sjos.12174
Publication status	Published - 1 Jun 2016

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10.1111/sjos.12174

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Cite this

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abstract = "Outlier detection algorithms are intimately connected with robust statistics that down-weight some observations to zero. We define a number of outlier detection algorithms related to the Huber-skip and least trimmed squares estimators, including the one-step Huber-skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.",

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AB - Outlier detection algorithms are intimately connected with robust statistics that down-weight some observations to zero. We define a number of outlier detection algorithms related to the Huber-skip and least trimmed squares estimators, including the one-step Huber-skip estimator and the forward search. Next, we review a recently developed asymptotic theory of these. Finally, we analyse the gauge, the fraction of wrongly detected outliers, for a number of outlier detection algorithms and establish an asymptotic normal and a Poisson theory for the gauge.

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