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Chen, S. (2020), A new distribution‐free k‐sample test: Analysis of kernel density functionals. Can J Statistics, 48: 167-186. doi:10.1002/cjs.11525
The author proposed a novel distribution-free k-sample test of differences in location shifts. The proposed test parallels traditional one-way ANOVA and the Kruskal-Wallis (KW) test aiming at testing locations of unknown distributions. Empirical simulation studies and real data example indicate that the proposed analysis of kernel density functional estimate (ANDFE) test is superior to existing competitors when the k groups differ mainly in location rather than shape for fat-tailed or heavy-tailed distributions, especially in unbalanced data. ANDFE is also highly recommended when it is unclear whether test groups are different mainly in shape or location. Furthermore, ANDFE, as a nonparametric version of ANOVA, can be extended to high-order models to test both main effects and interactions.