Almost sure central limit theorem for the products of U-statistics

Metrika ◽  
2009 ◽  
Vol 73 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Zuoxiang Peng ◽  
Zhongquan Tan ◽  
Saralees Nadarajah
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
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.

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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