Wilcox Rand R
Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061, USA.
Br J Math Stat Psychol. 2007 May;60(Pt 1):107-17. doi: 10.1348/000711006X98305.
A local measure of association that allows both heteroscedasticity and a non-linear association was developed during the 1990s. The basic goal is to measure the strength of the association between X and Y, given X, when Y = theta(X) + tau(X)epsilon for some unknown functions theta(X) and tau(X). Application of this method requires the estimation of the derivative of theta(X). The focus in this paper is on four alternatives to a very slight modification of the method used by Doksum et al. when estimating this derivative. The main result is that in simulations, a certain robust analogue of their method dominates in terms of mean squared error, even under normality. The bias of the method is found to be small but a little larger than the bias associated with the method used by Doksum et al. The method is based in part on bootstrap bagging followed by a lowess smooth.
20世纪90年代开发了一种局部关联度量方法，该方法允许异方差性和非线性关联。基本目标是在Y = theta(X) + tau(X)epsilon（其中theta(X)和tau(X)为某些未知函数）的情况下，给定X时测量X与Y之间关联的强度。应用此方法需要估计theta(X)的导数。本文重点关注对Doksum等人在估计此导数时所使用方法进行非常轻微修改后的四种替代方法。主要结果是，在模拟中，即使在正态性条件下，他们方法的某种稳健类似方法在均方误差方面占主导地位。发现该方法的偏差较小，但比Doksum等人使用的方法所关联的偏差略大。该方法部分基于自助聚合，然后进行局部加权散点平滑回归。
