通过求解三次方程的非参数相关性估计器及其在脑功能连接分析中的应用
Nonparametric Correlation Estimator via Solving Cubic Equations and its Application to Brain Functional Connectivity Analysis
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- Lijiang Culture and Tourism College（丽江文化旅游学院）
- York Neuroimaging Centre, University of York（约克大学神经影像中心）
- School of Mathematics, Statistics and Actuarial Science, University of Kent（肯特大学数学、统计与精算科学学院）
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中文总结 AI 辅助
本文提出一种基于三次方程求解的非参数相关性估计器，结合局部线性平滑修正边界效应，具备一致性和渐近正态性，并成功应用于六个频带下脑网络动态功能连接分析。
中文摘要 AI 辅助
本文提出了一种新颖的基于求解三次方程的相关性系数非参数估计器。该方法允许在非参数框架下估计时变相关性系数，为捕捉变量间的复杂关系提供了灵活性。此外，我们采用局部线性平滑技术来修正非参数估计中常见的边界效应。我们建立了所提出估计器的理论性质，包括一致性和渐近正态性，并通过模拟研究展示了其性能。另外，我们将该方法应用于分析六个频带下脑网络中的动态功能连接，突显了其在揭示神经交互和认知过程见解方面的潜力。
英文摘要
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.
