Adaptive nonparametric tests for a single sample location problem

Abstract

This paper considers a location test in a single sample setting without any assumption about the symmetry of the continuous distribution. Two adaptive test procedures are suggested — one is a probabilistic approach while the other is a deterministic approach. The deterministic approach is based on calculating a measure of symmetry and using it as a basis for choosing between the sign test and the Wilcoxon signed rank test. The probabilistic approach is also a combination of the sign test and the Wilcoxon signed rank test according to evidence of asymmetry provided by the P -value from the triples test for symmetry given in Randles et al. [R.H. Randles, M.A. Fligner, G.E. Policello, D.A. Wolfe, An asymptotically distribution-free test for symmetry versus asymmetry, Journal of the American Statistical Association 75 (1980) 168–172]. A simulation study shows that the proposed deterministic approach using a simple measure of symmetry is as good as Lemmer [H.H. Lemmer, Adaptive tests for the median, IEEE Transactions on Reliability 42 (1993) 442–448] in terms of power and attainment of the nominal size. The probabilistic approach has been shown to be superior to the other existing competitors.