Asymptotic properties of linear functions of order statistics
Let \(X_{r:n}\) be the r-th order statistic of a sample of size n. Let \(T_ n\) be the arithmetical mean of \(J(r/(n+1))h(X_{r:n})\), where both J(.) and h(.) are some smooth functions (specified in the paper). The authors establish an almost sure approximation to \(T_ n\), from which asymptotic normality and an iterated logarithm theorem are deduced.
scientific article; zbMATH DE number 4064245
scientific article