Almost sure invariance principles for empirical distribution functions of weakly dependent random variables

1976 ◽  
pp. 83-105
Author(s):  
Walter Philipp
Keyword(s):  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Dependent Random Variables ◽  
Invariance Principles ◽  
Weakly Dependent Random Variables ◽  
Weakly Dependent ◽  
Empirical Distribution Functions

scholarly journals Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

1997 ◽  
Vol 10 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Shan Sun ◽  
Ching-Yuan Chiang
Keyword(s):  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Limiting Behavior ◽  
U Statistics ◽  
Strongly Mixing ◽  
Almost Sure Representation ◽  
Mixing Sequences ◽  
Empirical Distribution Functions

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.

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