A Note on Modelling Cross-Correlations: Hyperbolic Secant Regression
本文提出一种新的双变量正态相关性估计量，能在样本量小至1时有效工作，并利用双曲正割变换实现对称分布，从而支持对相关性的回归建模而不损失分辨率。
The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered.It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value.A new estimator of a bivariate normal correlation is given that has useful performance down to samples of size one.This allows regression type modelling of the correlation without unnecessary loss of resolution.The arc-tanh transformation of this estimator has a symmetric Fisher's z-distribution about the arc-tanh correlation.A method of smoothing the correlation estimates is given using moving average smoothers of the sufficient statistics from which the correlation estimator is calculated.