次序统计量线性函数的强逼近

STRONG APPROXIMATION FOR LINEAR FUNCTION OF ORDER STATISTICS

设X_(n1)X_(n2)…X_(nk)为iid随机变量X_1…X_n的次序统计量,X_(ni)对C_(ni)的一种特殊情况,在一定的条件下,我们证明了T_n几乎处处收敛于一正态序列。

Let X_(n1)≤X_(n2)≤…≤X_(nn) be the order statistics of X_1…X_n iid r. v T_n=∑_(i=1)~n C_(ni) X_(ni). Under Some Conditions of C_(ni), We prove that T_n almost sure converge to a normal Sequence and obtaion the order of convergence.