A COMPLETE SOLUTION FOR WEAK CONVERGENCE OF HEAVILY TRIMMED SUMS

<正> Let {X_n, n≥1} be a sequence of iidrvs with a common df F and for every n, let Xn,1≤…≤Xn,n denote the order statistics of X1,…, X_n. Consider the sums S_n* =sum from k=k_n+1 to l_n（X_n,k）, n≥1, where k_n and l_n satisfy k_n/（n+1）→a and l_n/（n+1）→b for some 0*- （n+1） M(k_n/（n+1）, l_n/（n+1）)/（n+1）1/2 to converge weakly to a df G, where M（s, t） = integral from n=s to t(F-（w）dw) forr 0-（t） = inf{x:F（x）≥t}.