Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence

作者：Peng Zuoxiang^*; Wang Ping; Nadarajah Saralees

来源：Electronic Journal of Statistics, 2009, 3(0): 851-864.

DOI：10.1214/09-EJS443

• Almost sure limit theorem
• complete and incomplete samples
• limiting distribution
• maximum
• stationary Gaussian sequence

Let {X-k, k >= 1} be a stationary Gaussian sequence with partial maximum M-n = max{X-k, 1 <= k <= n} and sample mean (X) over bar (n) = Sigma(n)(k=1) X-k/n. Suppose that some of the random variables X-1, X-2, ... can be observed and the others not. Denote by (M) over tilde (n), the maximum of the observed random variables from the set {X-1, X-2, ... , X-n}. Under some mild conditions, we prove the joint limiting distribution and the almost sure limit theorem for ((M) over tilde - (X) over bar (n), M-n - (X) over bar (n)).

• 出版日期2009
• 单位西南大学