Almost sure convergence of extreme order statistics

作者：Peng Zuoxiang^*; Li Jiaona; Nadarajah Saralees

来源：Electronic Journal of Statistics, 2009, 3(0): 546-556.

DOI：10.1214/08-EJS303

• Almost sure convergence
• order statistics

Let M-n((k)) denote the kth largest maximum of a sample (X-1, X-2, ... , X-n) from parent X with continuous distribution. Assume there exist normalizing constants a(n) > 0, b(n) is an element of R and a nondegenerate distribution G such that a(n)(-1)(M-n((1)) - b(n)) ->(w) G. Then for fixed k is an element of N, the almost sure convergence of 1/D-N Sigma(N)(n=k)d(n)I{Mn-(1) <= a(n)x(1) b(n), Mn-(2) <= a(n)x(2) b(n), ... , Mn-(k) <= a(n)x(k) b(n)} is derived if the positive weight sequence (d(n)) with D-N Sigma(N)(n=1)d(n) satisfies conditions provided by Hormann. Some practical issues of this result are also discussed.

• 出版日期2009
• 单位东南大学