scholarly journals A Central Limit Theorem for incomplete U-statistics over triangular arrays

2021 ◽  
Vol 35 (3) ◽  
Author(s):  
Matthias Löwe ◽  
Sara Terveer
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
U Statistics ◽  
Triangular Arrays

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

scholarly journals A martingale central limit theorem without negligibility conditions

1978 ◽  
Vol 18 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Sufficient Conditions ◽  
Infinitely Divisible ◽  
Martingale Central Limit Theorem ◽  
Triangular Arrays ◽  
Infinitely Divisible Laws ◽  
Martingale Case

We obtain sufficient conditions for the convergence of martingale triangular arrays to infinitely divisible laws with finite variances, without making the usual assumptions of uniform asymptotic negligibility. Our results generalise known results for both the martingale case under a negligibility assumption and the classical (independence) case without such assumptions.

scholarly journals A central limit theorem for numbers satisfying a class of triangular arrays associated with Hermite polynomials

2021 ◽  
Vol 61 ◽  
pp. 1-7
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Generating Function ◽  
Limit Theorems ◽  
Hermite Polynomials ◽  
Triangular Arrays ◽  
Analytical Expressions

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.    

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