title: Local measures of association: estimating the derivative of the regression line.
abstract: 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.
authors.affiliation: Department of Psychology, University of Southern California, Los Angeles, CA 90089-1061, USA. rwilcox@usc.edu
authors.forename: Rand R
authors.initials: RR
authors.lastname: Wilcox
mesh_terms: D000704:Analysis of Variance; D006801:Humans; D016018:Least-Squares Analysis; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D012044:Regression Analysis; D013223:Statistics as Topic