EDGEWORTH EXPANSIONS OF DISTRIBUTION FUNCTIONS OF INDEPENDENT RANDOM VARIABLES

<正> Let X1,…,X_n be mutually independent （but may not be identically distributed） such that EXj=0, j=1, 2, …, n, B_n2=sum from j=1 to n EXj2>0 and sum from j=1 to n E|Xj|κ<∞, with integer κ≥3. The asymptotic expansion of the distribution function F_n（x） of B_n-1 sum from j=1 to n Xj is investigated in this paper. The ideal result of the non-uniform estimates of the residual term in this expansion is obtained. In passing, the non-aniform rate of the asymptotic normality of F_n（x） is established.