重截断和的渐近分布
ON THE ASYMPTOTIC DISTRIBUTION OF HEAVILY TRIMMED SUMS
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摘要: 设Xn,n≥1是i.i.d.随机变量序列,Xn,1≤…≤Xn,n是X1,…,Xn的次序统计量。又设kn,1, kn,2是满足条件1≤kn,1<kn,2≤n的整数而且对某0<a1<a2<1和某c1,c2∈R,有\lim _n \rightarrow \infty n^1 / 2\left(k_n, 1 / n-a_i\right)=c_i, i=1,2.本文给出了截断和S_n^*=\sum_j=k_n, 1^k_n, 1 X_n, j的渐近分布。我们的结果是Csörgö,Haeusler和Mason的一个定理的推广。Abstract: Let \left\X_n, n \geqslant 1\right\ be a sequence of i.i.d. r.v.'s and let X_n, 1 \leqslant X_n, 2 \leqslant \cdots \leqslant X_n, n be the order statistics of \mathrmX_1, \cdots, \mathrmX_n. Suppose that k_n, 1 and k_n, 2 are integers satisfying 1 \leqslant k_n, 1
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