Journal of Data Science

Abstract: It is well known that the ordinary least squares (OLS) regression estimator is not robust. Many robust regression estimators have been proposed and inferential methods based on these estimators have been derived. However, for two independent groups, let θj (X) be some conditional measure of location for the jth group, given X, based on some robust regression estimator. An issue that has not been addressed is computing a 1 − confidence interval for θ1(X) − θ2(X) in a manner that allows both within group and between group hetereoscedasticity. The paper reports the finite sample properties of a simple method for accomplishing this goal. Simulations indicate that, in terms of controlling the probability of a Type I error, the method performs very well for a wide range of situations, even with a relatively small sample size. In principle, any robust regression estimator can be used. The simulations are focused primarily on the Theil-Sen estimator, but some results using Yohai’s MM-estimator, as well as the Koenker and Bas sett quantile regression estimator, are noted. Data from the Well Elderly II study, dealing with measures of meaningful activity using the cortisol awakening response as a covariate, are used to illustrate that the choice between an extant method based on a nonparametric regression estimator, and the method suggested here, can make a practical difference.

Abstract: The paper considers the problem of comparing measures of lo cation associated with two dependent groups when values are missing at random, with an emphasis on robust measures of location. It is known that simply imputing missing values can be unsatisfactory when testing hypothe ses about means, so the goal here is to compare several alternative strategies that use all of the available data. Included are results on comparing means and a 20% trimmed mean. Yet another method is based on the usual median but differs from the other methods in a manner that is made obvious. (It is somewhat related to the formulation of the Wilcoxon-Mann-Whitney test for independent groups.) The strategies are compared in terms of Type I error probabilities and power.