Asymptotic normality for U-statistics of associated random variables

2001 ◽  
Vol 97 (2) ◽  
pp. 201-225 ◽  
Author(s):  
I. Dewan ◽  
B.L.S. Prakasa Rao
Keyword(s):  
Asymptotic Normality ◽  
Random Variables ◽  
Associated Random Variables ◽  
U Statistics

scholarly journals A Review on asymptotic normality of sums of associated random variables

2016 ◽  
Vol 11 (1) ◽  
pp. 855-867 ◽  
Author(s):  
Gane Samb LO ◽  
Harouna SANGARE ◽  
Cheikhna Hamallah NDIAYE
Keyword(s):  
Asymptotic Normality ◽  
Random Variables ◽  
Associated Random Variables

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.

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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