A large deviation result for signed linear rank statistics under the symmetry hypothesis
This paper investigates the convergence of normalized signed linear rank statistics \(S_ n\) to the Gaussian distribution for i.i.d. random variables the distribution of which is continuous and symmetric about zero. It considers the uniform convergence of distribution functions over intervals going to infinity slower than \(n^{1/4}:\) this can be called ''mean deviation'' but not large deviation theorem. The author considers unbounded score functions and improves the result of \textit{M. Seoh, S. Ralescu} and \textit{M. L. Puri} [Ann. Probab. 13, 115-125 (1985; Zbl 0558.62019)].
scientific article; zbMATH DE number 3998968