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Change-point analysis in increasing dimension

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  • Jirak, Moritz

Abstract

Let {Yk,k∈Z} be a d-dimensional stationary process, and g(d)=(g1(Y1,…Yn),…,gd(Y1,…Yn))t be a collection of estimators for some parameter Ψ(d)∈Rd. Based on the weighted CUSUM process, we discuss several procedures to detect possible changes in Ψ(d), where we explicitly allow d=dn to increase with the sample size n. It is demonstrated that an increase in dn (as n increases) may both lead to a loss or gain in power for testing procedures.

Suggested Citation

  • Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:136-159
    DOI: 10.1016/j.jmva.2012.05.007
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    References listed on IDEAS

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    1. Steland, Ansgar & von Sachs, Rainer, 2018. "Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2816-2855.
    2. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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