Asymptotic expansions for conditional distributions

AbstractIt is shown that—under appropriate regularity conditions—the conditional distribution of the first p components of a normalized sum of i.i.d. m-dimensional random vectors, given the complementary subvector, admits a Chebyshev-Cramér asymptotic expansion of order o(n−(s−2)2), uniformly over all Borelsets in Rp and uniformly in a region of the conditioning subvector that includes moderate deviations