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

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Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 122))

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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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Author information

Authors and Affiliations

  1. Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewa Skubalska-Rafajłowicz

Authors
  1. Ewa Skubalska-Rafajłowicz
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Corresponding author

Correspondence to Ewa Skubalska-Rafajłowicz .

Editor information

Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

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Skubalska-Rafajłowicz, E. (2015). Change-Point Detection of the Mean Vector with Fewer Observations than the Dimension Using Instantaneous Normal Random Projections. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_20

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