scholarly journals Asymptotic distributions of multivariate intermediate order statistics

1996 ◽  
Vol 41 (4) ◽  
pp. 840-853
Author(s):  
Shi Hong Cheng ◽  
Shi Hong Cheng ◽  
Лоренс де Хаан ◽  
Laurens de Haan ◽  
Jing Ping Yang ◽  
...  
Keyword(s):  
Order Statistics ◽  
Asymptotic Distributions ◽  
Intermediate Order Statistics ◽  
Intermediate Order

Almost sure limit theorem for the order statistics of stationary Gaussian sequences

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3355-3364 ◽  
Author(s):  
Yang Chen ◽  
Zhongquan Tan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Order Statistics ◽  
Central Limit ◽  
Almost Sure Limit Theorem ◽  
Extreme Order Statistics ◽  
Intermediate Order Statistics ◽  
Intermediate Order ◽  
Comparison Inequality

In this paper, by using a new comparison inequality for order statistics of Gaussian variables, we proved an almost sure central limit theorem for extreme order statistics of stationary Gaussian sequences with covariance rn under the condition rn log n(log log n)1+? = O(1) for some ? > 0. A similar result on intermediate order statistics is also proved for stationary Gaussian sequences. The obtained results improve some of the existing results.

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