Distribution-Free Tests

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Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “In fact, when d1 = d2 = 1, we show in Lemma 4.2 that our proposed test is exactly equivalent to the statistic put forward in Blum, Kiefer, and Rosenblatt (1961) which in turn is a modification of the celebrated Hoeffding’s D-statistic (Hoeffding (1948))— one of the first nonparametric tests for…”
A New Coefficient of Correlation (2019, background): “…1941; Rényi 1959; Breiman and Friedman 1985), various coefficients based on joint cumulative distribution functions and ranks (Hoeffding 1948; Blum, Kiefer, and Rosenblatt 1961; Yanagimoto 1970; Puri and Sen 1971; Rosenblatt 1975; Csörgő 1985; Romano 1988; Bergsma and Dassios 2014; Nandy,…”
Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs (2019, background): “…Hoeffding’s D (Hoeffding 1948) to multivariate cases, and Kim, Balakrishnan, and Wasserman (2020) proposed the analogues of Blum–Kiefer–Rosenblatt’s R (Blum, Kiefer, and Rosenblatt 1961) and Bergsma–Dassios– Yanagimoto’s τ ∗ (Yanagimoto 1970; Bergsma and Dassios 2014; Drton, Han, and Shi 2020).”