scholarly journals The Functional Law of the Iterated Logarithm for Stationary Strongly Mixing Sequences

1995 ◽  
Vol 23 (3) ◽  
pp. 1188-1203 ◽  
Author(s):  
Emmanuel Rio
Keyword(s):  
Iterated Logarithm ◽  
Strongly Mixing ◽  
Mixing Sequences

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.

scholarly journals On the accuracy of bootstrapping sample quantiles of strongly mixing sequences

2007 ◽  
Vol 82 (2) ◽  
pp. 263-282 ◽  
Author(s):  
Shuxia Sun
Keyword(s):  
Rate Of Convergence ◽  
Marginal Distribution ◽  
Regularity Conditions ◽  
One Dimensional ◽  
Strongly Mixing ◽  
Moving Block Bootstrap ◽  
Mixing Sequences ◽  
The One ◽  
Approximations To Distributions ◽  
Sample Quantiles

AbstractIn this paper, we examine the rate of convergence of moving block bootstrap (MBB) approximations to the distributions of normalized sample quantiles based on strongly mixing observations. Under suitable smoothness and regularity conditions on the one-dimensional marginal distribution function, the rate of convergence of the MBB approximations to distributions of centered and scaled sample quantiles is of order O(n−1¼ log logn).

scholarly journals Chover-type laws of the iterated logarithm for weighted sums of ρ∗-mixing sequences

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
Guang-hui Cai
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Type Result ◽  
Stable Law ◽  
Iterated Logarithm ◽  
Mixing Sequences

To derive a Baum-Katz-type result, we establish a Chover-type law of the iterated logarithm for the weighted sums of ρ∗-mixing and identically distributed random variables with a distribution in the domain of a stable law. Our result obtained not only generalizes the main results of Peng and Qi (2003) and Qi and Cheng (1996) to ρ∗-mixing sequences of random variables, but also improves them.

Sign in / Sign up

Export Citation Format

Share Document