Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
Abstract
In this paper, we propose a novel nonparametric estimator for the correlation coefficient that is based on solving a cubic equation. This approach allows for the estimation of time-varying correlation coefficients in a nonparametric framework, providing flexibility in capturing complex relationships between variables. Furthermore, we adopt the local linear smoothing technique to correct the boundary effects, which are common in nonparametric estimation. We establish the theoretical properties of the proposed estimator, including consistency and asymptotic normality, and demonstrate its performance through simulation studies. Additionally, we apply our method to analyse dynamic functional connectivity in brain networks under six frequency bands, highlighting its potential for uncovering insights into neural interactions and cognitive processes.
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BibTeX
@misc{yang2026nonparametric,
title = {{Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis}},
author = {Shenyuan Yang and Gary Green and Jian Zhang and André Gouws and Jie Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13848},
eprint = {2609.13848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13848},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
AU - Shenyuan Yang
AU - Gary Green
AU - Jian Zhang
AU - André Gouws
AU - Jie Li
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13848
UR - https://arxiv.org/abs/2609.13848
AB - In this paper, we propose a novel nonparametric estimator for the correlation coefficient that is based on solving a cubic equation. This approach allows for the estimation of time-varying correlation coefficients in a nonparametric framework, providing flexibility in capturing complex relationships between variables. Furthermore, we adopt the local linear smoothing technique to correct the boundary effects, which are common in nonparametric estimation. We establish the theoretical properties of the proposed estimator, including consistency and asymptotic normality, and demonstrate its performance through simulation studies. Additionally, we apply our method to analyse dynamic functional connectivity in brain networks under six frequency bands, highlighting its potential for uncovering insights into neural interactions and cognitive processes.
ER -