Permutation Variation and Alternative Hyper-Sphere Decomposition

Qingze Li and Jianxin Pan
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Qingze Li: School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
Jianxin Pan: Research Center for Mathematics, Beijing Normal University at Zhuhai, Zhuhai 519087, China

Mathematics, 2022, vol. 10, issue 4, 1-19

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.

Keywords: order dependency; alternative Hyper-sphere decomposition; permutation invariant; unconstrained parameterization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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