文章基本信息

标题：Comparing the Strength of Association of Two Predictors via Smoothers or Robust Regression Estimators
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作者：Wilcox, Rand R.
期刊名称：Journal of Modern Applied Statistical Methods
出版年度：2011
卷号：10
期号：1
页码：3
出版社：Wayne State University
摘要：Consider three random variables, Y , X1 and X2, having some unknown trivariate distribution and let n2j (j = 1, 2) be some measure of the strength of association between Y and Xj. When n2j is taken to be Pearson’s correlation numerous methods for testing Ho : n21 = n22 have been proposed. However, Pearson’s correlation is not robust and the methods for testing H0 are not level robust in general. This article examines methods for testing H0 based on a robust fit. The first approach assumes a linear model and the second approach uses a nonparametric regression estimator that provides a flexible way of dealing with curvature. The focus is on the Theil-Sen estimator and Cleveland’s LOESS smoother. It is found that a basic percentile bootstrap method avoids Type I errors that exceed the nominal level. However, situations are identified where this approach results in Type I error probabilities well below the nominal level. Adjustments are suggested for dealing with this problem.
关键词：Explanatory power; Theil-Sen estimator; nonparametric regression; bootstrap methods; kernel density estimators.