Browse Journals

Let  be some conditional measure of location associated with the random variable Y, given X. Many nonparametric regression estimators of  have been proposed. One that is particularly convenient when dealing with robust measures of location is a running interval smoother. The paper deals with the goal of computing K confidence intervals for  corresponding to K values of the covariate X, where K is relatively large, that have simultaneous probability coverage When working with a 20% trimmed mean, methods based on the Studentized maximum modulus distribution or the Bonferroni method, for example, can be highly unsatisfactory. The paper describes and compares methods that provide more satisfactory results. When  is taken to be the median of Y, given X, the approach based on 20% trimmed means performs poorly. An alternative approach, based in part on the Bonferroni method, was found that gives reasonably satisfactory results. It is illustrated that achieving reasonably accurate probability coverage depends in part on the choice for the span and that a good choice for the span is a function of the strength of the association. 

confidence band, smoothers, robust regression, trimmed mean.