Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II

By V. Dupac, J. Hájek. 1968

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Asymptotic Theory for Random Forests (2014, methodology): “The ideas used in our proof go back to techniques developed by Hoeﬀding [21] and H´ajek et al. [17] to establish the We begin by brieﬂy reviewing their results to give some context to our proof.”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE I. OPTIMAL RANK-BASED TESTS FOR SPHERICITY (2006, unknown): “1 in [14]) applies (conditional on U), yielding for all [with appropriate r and s, m K := 1 n ∑n i=1 K( i n+1) and σ 2 K := ∫ 1 0 K 2(u) du − (∫ 1 0 K(u)du)2],”
Stein's Method and Stochastic Analysis of Rademacher Functionals (2008, background): “Indeed there is a long history of normal approximations for finite vectors; notably Hoeffding decompositions, also in conjunction with truncations such as Hajek’s projection, can yield optimal Berry-Esséen bounds, see [3] and [18] as well [46] for some seminal papers.”
Ranking the Best Instances (2006, background): “refer to Hájek and Sidák (1967), Dupac and Hájek (1969), Koul (1970), and Koul and R.G. Staudte (1972) for an account on rank statistics.”
Visualization and exploration of high-dimensional functions using the functional anova decomposition (1996, background): “Efron and Steinprovide a number of references to earlier work relating to functional ANOVA (Haj ek,1968; Hoe ding, 1948; Mallows, 1975; Rubin and Vitale, 1980).”