Limiting distributions for statistics based on different samples

Let A m and B n be two k-dimensional statistics based on independent samples of sizes m and n, respectively, from two populations, and let f be a vector valued function defined on the 2k-th Euclidean space. This paper deals with the limiting distribution function of f(A m ,B n ), suitably normalized, as m and n tend to infinity separately. Applications to estimation and hypothesis testing problems are given. The connection between these results and those previously obtained in the literature is discussed.