Efficient algorithms for the sensitivities of the Pearson correlation coefficient and its statistical significance to online data
在线新增数据对皮尔逊相关系数及其显著性影响的高效算法
Reliably measuring the collinearity of bivariate data is crucial in statistics, particularly for time-series analysis or ongoing studies in which incoming observations can significantly impact current collinearity estimates. Leveraging identities from Welford's online algorithm for sample variance, we develop a rigorous theoretical framework for analyzing the maximal change to the Pearson correlation coefficient and its p-value that can be induced by additional data.…