Corrigendum to “Central limit theorem for U-statistics of associated random variables” [Statist. Probab. Lett. 57 (1) (2002) 9–15]

2015 ◽  
Vol 106 ◽  
pp. 147-148 ◽  
Author(s):  
Isha Dewan ◽  
B.L.S. Prakasa Rao
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Associated Random Variables ◽  
U Statistics

Asymptotic normality of some Graph-Related statistics

1989 ◽  
Vol 26 (1) ◽  
pp. 171-175 ◽  
Author(s):  
Pierre Baldi ◽  
Yosef Rinott
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Simple Proof ◽  
Random Function ◽  
Random Variables ◽  
Local Maxima ◽  
Colored Graphs ◽  
U Statistics

Petrovskaya and Leontovich (1982) proved a central limit theorem for sums of dependent random variables indexed by a graph. We apply this theorem to obtain asymptotic normality for the number of local maxima of a random function on certain graphs and for the number of edges having the same color at both endpoints in randomly colored graphs. We briefly motivate these problems, and conclude with a simple proof of the asymptotic normality of certain U-statistics.

scholarly journals The Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanying Jiang ◽  
Qunying Wu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Associated Sequences ◽  
Local Central Limit Theorem

In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables:limn→∞(1/logn)∑k=1n(I(ak≤Sk<bk)/k)P(ak≤Sk<bk)=1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central limit theorems from the i.i.d. case to the stationary negatively associated sequences.

scholarly journals Almost sure central limit theorems for strongly mixing and associated random variables

2002 ◽  
Vol 29 (3) ◽  
pp. 125-131 ◽  
Author(s):  
Khurelbaatar Gonchigdanzan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Mixing Rate ◽  
Associated Random Variables ◽  
Strongly Mixing ◽  
Slow Mixing ◽  
Mixing Sequence

We prove an almost sure central limit theorem (ASCLT) for strongly mixing sequence of random variables with a slightly slow mixing rateα(n)=O((loglogn)−1−δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.

scholarly journals Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1413-1422 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
The Self ◽  
Partial Sums ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

Let X,X1,X2,... be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the self-normalized partial sums Sn/Vn is established, where: Sn = ?ni=1 Xi,V2n = ?ni=1 X2i .

Asymptotic normality of some Graph-Related statistics

1989 ◽  
Vol 26 (01) ◽  
pp. 171-175 ◽  
Author(s):  
Pierre Baldi ◽  
Yosef Rinott
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Simple Proof ◽  
Random Function ◽  
Random Variables ◽  
Local Maxima ◽  
Colored Graphs ◽  
U Statistics

Petrovskaya and Leontovich (1982) proved a central limit theorem for sums of dependent random variables indexed by a graph. We apply this theorem to obtain asymptotic normality for the number of local maxima of a random function on certain graphs and for the number of edges having the same color at both endpoints in randomly colored graphs. We briefly motivate these problems, and conclude with a simple proof of the asymptotic normality of certain U-statistics.

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