Almost sure central limit theorem for the location and height of extreme order statistics and high values

2019 ◽  
pp. 1-14
Author(s):  
Luyun Ding ◽  
Zhongquan Tan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Order Statistics ◽  
Central Limit ◽  
Extreme Order Statistics

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.

scholarly journals Almost Sure Central Limit Theorem of Sample Quantiles

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Yu Miao ◽  
Shoufang Xu ◽  
Ang Peng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Order Statistics ◽  
Central Limit ◽  
Sample Quantiles

We obtain the almost sure central limit theorem (ASCLT) of sample quantiles. Furthermore, based on the method, the ASCLT of order statistics is also proved.

An extension of almost sure central limit theorem for order statistics

Extremes ◽  
2008 ◽  
Vol 12 (3) ◽  
pp. 201-209 ◽  
Author(s):  
Tong Bin ◽  
Peng Zuoxiang ◽  
Saralees Nadarajah
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Order Statistics ◽  
Central Limit

scholarly journals On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Almost Sure Convergence ◽  
First Passage Percolation ◽  
First Passage ◽  
Percolation Problem ◽  
Vertex Set ◽  
Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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