Asymptotic distributions of maxima of complete and incomplete samples from strongly dependent stationary Gaussian sequences

作者：Cao Lunfeng; Peng Zuoxiang^*

来源：Applied Mathematics Letters, 2011, 24(2): 243-247.

DOI：10.1016/j.aml.2010.09.012

• Asymptotic distribution
• Maximum
• Strongly dependent stationary Gaussian sequence
• Missing data

Let (X(n)) be a stationary Gaussian sequence with mean 0 and variance 1. Let r(n) = E(X(1)X(n+1)) and M = max {X((k) under tilde) 1 <= k <= n}. Suppose that some of the random variables of (X(n)) can be observed and let M(n) denote the partial maximum of the observed variables. In this note, we study the limiting distribution of random vector ((M) over tilde (n), M(n)) for the strongly dependent case where r(n) is convex with r(n) = o(1) and (r(n) log n)(-1) is monotone with (r(n) log n)(-1) = o(1).

• 出版日期2011-2
• 单位西南大学