Nonuniform Rates of Convergence to Normality for Two-Sample U-Statistics in Non IID Case with Applications

2013 ◽  
pp. 61-88 ◽  
Author(s):  
Ratan Dasgupta
Keyword(s):  
Rates Of Convergence ◽  
U Statistics

scholarly journals Rates of convergence for U-Statistics with varying kernels

1980 ◽  
Vol 21 (1) ◽  
pp. 1-5 ◽  
Author(s):  
N.C. Weber
Keyword(s):  
Distribution Function ◽  
Rates Of Convergence ◽  
U Statistics ◽  
Standard Normal Variable ◽  
Normal Variable ◽  
Standard Normal

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).

scholarly journals Rates of strong convergence for U-statistics in finite populations

1991 ◽  
Vol 50 (3) ◽  
pp. 468-480
Author(s):  
P. N. Kokic ◽  
N. C. Weber
Keyword(s):  
Strong Convergence ◽  
Random Sample ◽  
Finite Population ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Simple Random Sample ◽  
Finite Populations ◽  
Strong Law ◽  
U Statistics ◽  
Convergence Results

AbstractLet UNn be a U-statistic based on a simple random sample of size n selected without replacement from a finite population of size N. Rates of convergence results in the strong law are obtained for UNn, which are similar to those known for classical U-statistics based on samples of independent and identically distributed (iid) random variables.

scholarly journals Rates of convergence for random forests via generalized U-statistics

2022 ◽  
Vol 16 (1) ◽  
Author(s):  
Wei Peng ◽  
Tim Coleman ◽  
Lucas Mentch
Keyword(s):  
Random Forests ◽  
Rates Of Convergence ◽  
U Statistics
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