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Test for bandedness of high-dimensional precision matrices

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  • Guanghui Cheng
  • Zhengjun Zhang
  • Baoxue Zhang

Abstract

Statistical inferences in high-dimensional precision matrices are equally important as statistical inferences in high-dimensional covariance matrices. In the literature, much attention has been paid to the latter, and significant advances have been achieved, especially in estimation and test of the banded structure. This paper proposes a new test for testing banded structures of precision matrices without assuming any specific parametric distribution. The test is adapted to the large p small n problems in which we derive the asymptotic distribution under the null hypothesis of bandedness. Simulation results show that the proposed test performs well with finite sample sizes. A real data application is realised to a phone call centre data.

Suggested Citation

  • Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:884-902
    DOI: 10.1080/10485252.2017.1375112
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