重截断和的渐近分布  

ON THE ASYMPTOTIC DISTRIBUTION OF HEAVILY TRIMMED SUMS

作　　者：程士宏[1] 

机构地区：[1]北京大学

出　　处：《应用概率统计》1990年第4期387-394,共8页Chinese Journal of Applied Probability and Statistics

摘　　要：设{X_n,n≥1}是i.i.d.随机变量序列,X_n,1≤…≤X_(n,n)是X_1,…,X_n的次序统计量。又设k_(n,1,) k_(n,2)是满足条件1≤k_(n,1)<k_(n,2)≤n的整数而且对某0<a_1<a_2<1和某c_1,C_2∈R,有■n^(1/2)(k_n,i/n-a_i)=c_i,i=1,2.本文给出了截断和S_n~*=sum from j=k_(m,l) to k_(n,s) X_(n,j)的渐近分布。我们的结果是Csorgo,Haeusler和Mason的一个定理的推广。Let {X_n, n≥1} be a sequence of i. i. d. r. v. 's and let X_(n,1)≤X_(n, 2)≤…≤X_(n, n) be the order statistics of X_1, …, X_n. Suppose that k_(n, 1) and k_(n, 2) are integers satisfying 1≤k_(n, 1)<k_(n,2)≤n for each n≥1 and that lim n^(1/2)(k_(n,t)/n-a_i)=c_i, i=1, 2 for some 0<a_1<a_2<1 and some c_1, c_2∈R as n→∞. This paper is to give the asymptotic distribution of the trimmed sum sum form j=k_n,1 to k_n, 2 X_(n, j).Our results are the extension of Csorgo, Haeusler and Mason's theorem.

关 键 词：次序统计量 重截断和 渐近分布 

分 类 号：O212[理学—概率论与数理统计]