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Limit theorems for empirical processes based on dependent data


 
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1. Title Title of document Limit theorems for empirical processes based on dependent data
 
2. Creator Author's name, affiliation, country Patrizia Berti; University of Modena and Reggio-Emilia; Italy
 
2. Creator Author's name, affiliation, country Luca Pratelli; Accademia Navale di Livorno; Italy
 
2. Creator Author's name, affiliation, country Pietro Rigo; University of Pavia; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) conditional identity in distribution; empirical process; exchangeability; predictive measure; stable convergence
 
3. Subject Subject classification 60B10; 60F05; 60G09; 60G57
 
4. Description Abstract

Let $(X_n)$ be any sequence of random variables adapted to a filtration $(\mathcal{G}_n)$. Define $a_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid\mathcal{G}_n\bigr)$, $b_n=\frac{1}{n}\sum_{i=0}^{n-1}a_i$, and $\mu_n=\frac{1}{n}\,\sum_{i=1}^n\delta_{X_i}$. Convergence in distribution of the empirical processes $$ B_n=\sqrt{n}\,(\mu_n-b_n)\quad\text{and}\quad C_n=\sqrt{n}\,(\mu_n-a_n)$$ is investigated under uniform distance. If $(X_n)$ is conditionally identically distributed, convergence of $B_n$ and $C_n$ is studied according to Meyer-Zheng as well. Some CLTs, both uniform and non uniform, are proved. In addition, various examples and a characterization of conditionally identically distributed sequences are given.
 
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7. Date (YYYY-MM-DD) 2012-01-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1765
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1765
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
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