平稳随机序列的变秩顺序统计量的联合渐近分布

ON LIMITING JOINT DISTRIBUTIONS OF ORDER STATISTICS WITH VARIABLE RANKS FROM STATIONARY SEQUENCES

摘要: 设X_n是平稳序列,X₁^（n）≤…≤X_n^（n）是X₁…X_n的顺序统计量。k_n（r）,r=1,2是二变秩序列。本文在某种相关条件限制下得到了X_kn（1）^（n）,X_{n-kn（2）+1}^（n）)的极限分布。特别地,对满足k_n（r）/n→λ（r）∈0,1),r=1,2的特殊秩序列,得到了X_kn（1）^（n）,X_{n-kn（2）+1}^（n）)的所有可能的极限分布类。

Abstract: LetX_nbe a stationary sequence andX₁^（n）≤…≤X_n^（n）the order statistics of X₁…X_n. In this paper. We obtained a natural dependence restriction under which the limiting distributions of X_kn（1）^（n）,X_{n-kn（2）+1}^（n）) are determined where k_n（r）, r=1, 2 are two variable rank sequences In particular, the results for some special rank sequences k_n（r）, r=1, 2 satisfying k_n（r）/n→λ（r）∈0, 1), r=1, 2 are also obtained.