Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Yang, Shenyuan, Green, Gary, Zhang, Jian, Gouws, André, Li, Jie
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213229394
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