| dc.description.abstract | Let XI, X2, - - - be a sequence of independent and identically distributed
random variables with the common distribution being uniform on [0, 1].
Let Y1, Y2, * * - be a sequence of i.i.d. variables with continuous cdf F(t) and
with [0, 1] support. Let Fn(t, wo) denote the empirical distribution function
based on Yi(w), * * *, Yn(w) and let Gm(t, w) the empirical cdf pertaining to
X1(@), * * *, Xm(a(). Let supogt?j JF(t) - tj = i and Dn = supostsl i Fn(t, o1) -
tl. The limiting distribution of ni(Dn - i) is obtained in this paper. The
limiting distributions under the alternative of the corresponding one-sided
statistic in the one-sample case and the corresponding Smirnov statistics in
the two-sample case are also derived. The asymptotic distributions under
the alternative of Kuiper's statistic are also obtained. | |
