Advances and Applications in Statistics
Volume 1, Issue 1, Pages 27 - 48
(April 2001)
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LIMITING DISTRIBUTIONS FOR STATISTICS BASED ON DIFFERENT SAMPLES
Shaul K. Bar-Lev (Israel), Naftali A. Langberg (Israel) and Benjamin Reiser (Israel)
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and
be two k-dimensional
statistics based on independent samples of sizes m
and n,
respectively, from two populations, and let
be
a vector valued function defined on the 2k-th
Euclidean space. This paper deals with the limiting
distribution function of
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.