摘要
In simple linear regression with response variable Y and covariate X, the classical Pearson correlation measures the strength of the linear association between Y and X, and corresponds to the standardized slope of the regression line. This paper explores the concept of local linear correlation to capture the locally linear association between Y and X as a function of X, while preserving key properties of the Pearson correlation. Without assuming a parametric form for the joint distribution of (X, Y ), we show that the kernel-weighted local linear correlation measures the strength of locally linear association, and is connected to local linear regression through its interpretation as a locally standardized slope. We derive the finite-sample and asymptotic properties of the population and sample versions of local linear correlations and the optimal order of the bandwidth is provided. Numerical results confirm the asymptotic theory and a baseball data example is given for illustration. © Brazilian Statistical Association, 2026.
