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2015 | OriginalPaper | Buchkapitel

20. Change-Point Detection of the Mean Vector with Fewer Observations than the Dimension Using Instantaneous Normal Random Projections

verfasst von : Ewa Skubalska-Rafajłowicz

Erschienen in: Stochastic Models, Statistics and Their Applications

Verlag: Springer International Publishing

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Abstract

Our aim in this paper is to propose a simple method of a change-point detection of mean vector when the number of samples (historical data set) is smaller than the dimension. We restrict here our attention to the problem of monitoring independent individual observations under normality assumption. The presented approach is based on the Hotelling statistic. This statistic is applied to the data set projected onto a randomly chosen subspace of a sufficiently smaller dimension. We propose the procedure of normal random projection of data (historical data set and a new observation) instantaneously, just after a new observation appears. Next, we provide a model of the changes in the mean vector and derive the distribution of noncentrality parameter values. Further, a non-local power of the Hotelling test performed on projected samples is defined, which is the criterion for selecting the dimensionality of a projection subspace. Finally, simulation results are provided.

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Titel: Change-Point Detection of the Mean Vector with Fewer Observations than the Dimension Using Instantaneous Normal Random Projections
verfasst von: Ewa Skubalska-Rafajłowicz
Verlag: Springer International Publishing
Buch: Stochastic Models, Statistics and Their Applications
Print ISBN: 978-3-319-13880-0

Electronic ISBN: 978-3-319-13881-7

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-13881-7_20

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