An outlier test for linear processes
type: Item
instance of: scholarly article
title: An outlier test for linear processes
zbMATH Open document ID: 0778.62081
DOI: 10.1007/BF02613694
author: Thomas Flak
author: Wolfgang Schmid
published in: Metrika
publication date: 1993-10-18T00:00:00Z
full work available at URL: https://eudml.org/doc/176477
review text: Let \(Y_ 1,\ldots,Y_ n\) be an undisturbed linear process. An observed process \(X_ 1,\ldots,X_ n\) coincides with \(Y_ 1,\ldots,Y_ n\) except for some outliers. Let \(s_ n\) be an upper bound for the total number of outliers. The authors consider an outlier test based on the statistic \[ T_ n = \max_{1 \leq \mu(1)<\cdots< \mu(s_ n) \leq n} \sum^{s_ n}_{i=1} \bigl( X_{\mu(i)} -\hat Y_{\mu(i)} \bigr)^ 2 \] where \(\hat Y_ t\) is a predictor of \(Y_ t\). It is assumed that \(s_ n \to \infty\), \(s_ n/n \to 0\) and that the distribution of the squared standardized white noise belongs to a subset of the domain of attraction of the Gumbel distribution; the Gaussian white noise is included. The asymptotic distribution of \(T_ n\) under the null hypothesis `no outlier' is derived.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 425405
zbMATH Keywords: robust estimates
zbMATH Keywords: linear process
zbMATH Keywords: observed process
zbMATH Keywords: outlier test
zbMATH Keywords: squared standardized white noise
zbMATH Keywords: domain of attraction
zbMATH Keywords: Gumbel distribution
zbMATH Keywords: Gaussian white noise
reviewed by: Jiří Anděl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 425405