Consistency of the true correlation matrix estimator in generalized estimating equations for high-dimensional longitudinal data

Xianbin Chen; Donghai Peng; Xianbin Chen; Donghai Peng

doi:10.3934/math.20261304

AIMS Mathematics

2026, Volume 11, Issue 10: 33333-33349. doi: 10.3934/math.20261304

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Research article

Consistency of the true correlation matrix estimator in generalized estimating equations for high-dimensional longitudinal data

Xianbin Chen ^,,
Donghai Peng

Innovation and Entrepreneurship College, Zhongshan Polytechnic, Zhongshan, 528400, China

Received: 26 June 2026 Revised: 22 September 2026 Accepted: 09 October 2026 Published: 14 October 2026
MSC : 62E20, 62F12, 62J12

In this study, we consider the estimator of true correlation matrix within generalized estimating equations for high-dimensional longitudinal data. More precisely, a modified unit correlation matrix structure is constructed, and initial estimator during the iterative procedure is derived. Under mild regularity conditions, we establish the asymptotic consistency of the true correlation matrix estimator by techniques including the existence theorem of roots and Markov's inequality. Finally, we also perform some Monte Carlo studies to illustrate the theoretical analysis. The main result in this paper extends existing high-dimensional GEE theory to the multinomial response variable case.
- generalized estimating equations,
- true correlation matrix,
- consistency,
- multinomial response variable,
- high-dimensional longitudinal data
Citation: Xianbin Chen, Donghai Peng. Consistency of the true correlation matrix estimator in generalized estimating equations for high-dimensional longitudinal data[J]. AIMS Mathematics, 2026, 11(10): 33333-33349. doi: 10.3934/math.20261304

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Abstract

In this study, we consider the estimator of true correlation matrix within generalized estimating equations for high-dimensional longitudinal data. More precisely, a modified unit correlation matrix structure is constructed, and initial estimator during the iterative procedure is derived. Under mild regularity conditions, we establish the asymptotic consistency of the true correlation matrix estimator by techniques including the existence theorem of roots and Markov's inequality. Finally, we also perform some Monte Carlo studies to illustrate the theoretical analysis. The main result in this paper extends existing high-dimensional GEE theory to the multinomial response variable case.

References

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