An invariance principle for U-statistics in simple random sampling without replacement
Supplementing the well-known invariance principle for U-statistics based on i.i.d. observations [\textit{R. G. Miller} and \textit{P. K. Sen}, Ann. Math. Stat. 43, 31-41 (1972; Zbl 0238.62057)] we establish an invariance pinciple for U-statistics in case of simple random sampling from a sequence of finite populations. This generalizes the asymptotic normality result of \textit{H. K. Nandi} and \textit{P. K. Sen} [Calcutta Stat. Assoc. Bull. 12, 124-148 (1963; Zbl 0123.370)], and permits e.g. to prove asymptotic normality of U-statistics in the presence of random non- response.
simple random sampling without replacement
scientific article; zbMATH DE number 4064240