检验基因共表达结构中年龄的独立影响
Test of partial effects for Frechet regression on Bures-Wasserstein manifolds
- 基于弗雷歇回归与布雷斯-瓦萨里斯流形设计新检验方法
- 统计量渐近服从加权卡方混合分布，理论有效且一致
- 适用于单细胞数据中协变量偏效应的严格检验
我们提出一种新方法，用于检验弗雷歇回归中响应变量位于布雷斯-瓦萨里斯流形上的部分效应。在零假设下，该统计量可近似为退化V统计量，其极限分布为加权卡方随机变量的混合，权重由再生核希尔伯特空间（RKHS）核相关积分算子的特征值决定。我们建立了该检验的渐近有效性与一致性。通过模拟研究评估了其有限样本表现，并应用于单细胞数据，分析年龄在控制其他协变量后对基因共表达结构的影响。
原文摘要 · Abstract (English)
We propose a novel test for assessing partial effects in Fréchet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.
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