Nonparametric ANOVA using kernel methods

Abstract

A new approach to one-way and two-way analysis of variance from the nonparametric view point is introduced and studied. It is nonparametric in the sense that no distributional format assumed and the testing pertain to location and scale parameters. In contrast to the rank transformed approach, the new approach uses the measurement responses along with the highly recognized kernel density estimation, and thus called "kernel transformed" approach. Firstly, a novel kernel transformed approach to test the homogeneity of scale parameters of a group of populations with unknown distributions is provided. When homogeneity of scales is not rejected, we proceed to develop a one-way ANOVA for testing equality of location parameters and a generalized way that handles the two-way layout with interaction. The proposed methods are asymptotically F distributed. Simulation is used to compare the empirical significance level and the empirical power of our technique with the usual parametric approach. It is demonstrated that in the Normal Case, our method is very close to the standard ANOVA. While for other distributions that are heavy tailed (Cauchy) or skewed (Log-normal) our method has better empirical significance level close to the nominal level a and the empirical power of our technique are far superior to that of the standard ANOVA.