Robust ANCOVA: Some Small-sample Results when there are Multiple Groups and Multiple Covariates

Rand R. Wilcox

Journal of Applied Statistics, 2007, vol. 34, issue 3, 353-364

Abstract: Numerous methods have been proposed for dealing with the serious practical problems associated with the conventional analysis of covariance method, with an emphasis on comparing two groups when there is a single covariate. Recently, Wilcox (2005a: section 11.8.2) outlined a method for handling multiple covariates that allows nonlinearity and heteroscedasticity. The method is readily extended to multiple groups, but nothing is known about its small-sample properties. This paper compares three variations of the method, each method based on one of three measures of location: means, medians and 20% trimmed means. The methods based on a 20% trimmed mean or median are found to avoid Type I error probabilities well above the nominal level, but the method based on medians can be too conservative in various situations; using a 20% trimmed mean gave the best results in terms of Type I errors. The methods are based in part on a running interval smoother approximation of the regression surface. Included are comments on required sample sizes that are relevant to the so-called curse of dimensionality.

Keywords: Robust methods; smoothers; heteroscedasticity; curse of dimensionality (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1080/02664760601005053

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