Comparison of two types of confidence intervals based on Wilcoxon-type R-estimators

Omelka [Omelka, M., 2007. Second-order linearity of Wilcoxon rank statistics. Ann. Inst. Statist. Math. 59, 385-402] proposed an alternative way of constructing a confidence interval based on R-estimators for single parameters in linear models. We will compare this confidence interval with a traditional (Wald type) confidence interval theoretically as well as by means of a Monte Carlo experiment. As a by-product we will show the asymptotic normality of the estimator of ∫f2 proposed in [Koul, H.L., Sievers, G.L., McKean, J., 1987. An estimator of the scale parameter for the rank analysis of linear models under general score functions. Scand. J. Statist. 14, 131-141] under somewhat different assumptions from those in [Thewarepperuma, P.S., 1987. On estimation of some density functionals under regression and one sample models. Ph.D. Thesis. Michigan State University, Department of Statistics and Probability].