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Permutation Variation and Alternative Hyper-Sphere Decomposition

Author

Listed:
  • Qingze Li

    (School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
    These authors contributed equally to this work.)

  • Jianxin Pan

    (Research Center for Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, China
    Division of Science and Technology, United International College (BNU-HKBU), Zhuhai 519087, China
    These authors contributed equally to this work.)

Abstract

Current covariance modeling methods work well in longitudinal data analysis. In the analysis of data with no nature order, a common covariance modeling method would be inadequate. In this paper, a study is implemented to investigate the effects of permutations of data on the estimation of covariance matrix Σ . Based on the Hyper-sphere decomposition method (HPC), this study suggests that the change of data’s permutation breaks the consistency of covariance estimation. An alternative Hyper-sphere decomposition method with permutation invariant is introduced later in this paper. The alternative method’s consistency and asymptotic normality are studied when the observations follow a normal distribution. These results are tested using some example studies. Furthermore, a real data analysis is conducted for illustration purposes.

Suggested Citation

  • Qingze Li & Jianxin Pan, 2022. "Permutation Variation and Alternative Hyper-Sphere Decomposition," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:562-:d:747152
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    References listed on IDEAS

    as
    1. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    2. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    3. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
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