Hadamard differentiability on \(D[0,1]^p\)
The asymptotic normality of a statistical functional via the Hadamard derivative for univariate observations has been studied by \textit{J. A. Reeds} [On the definition of von Mises functionals. Ph.D. Diss., Harvard Univ., Cambridge, MA (1976)] and \textit{L. T. Fernholz} [Von Mises calculus for statistical functionals. (1983; Zbl 0525.62031)]. We generalize their methods to multivariate observations. We show that a statistical functional is asymptotically normal if it induces a Hadamard differentiable functional defined on the space \(D[0,1]^p\). This work involves \(p\)-dimensional empirical processes. As an example we illustrate the use of the von Mises method [\textit{R. von Mises}, Ann. Math. Stat. 18, 309-348 (1947; Zbl 0037.08401)] in proving the asymptotic normality of Spearman's rank correlation coefficient.
scientific article; zbMATH DE number 844598