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Moderate deviations for stable Markov chains and regression models

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1.	Title	Title of document	Moderate deviations for stable Markov chains and regression models
2.	Creator	Author's name, affiliation, country	Julien Worms; Universit'e de Marne La Vall'ee
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Large and Moderate Deviations, Martingales, Markov Chains, Least Squares Estimator for a regression model.
3.	Subject	Subject classification	60F10 ; 60J10 ; 62J05 ; 62J02.
4.	Description	Abstract	We prove moderate deviations principles for unbounded additive functionals of the form $S_n = \sum_{j=1}^{n} g(X^{(p)}_{j-1})$, where $(X_n)_{n\in N}$ is a stable $R^d$-valued functional autoregressive model of order $p$ with white noise and stationary distribution $\mu$, and $g$ is an $R^q$-valued Lipschitz function of order $(r,s)$; the error of the least squares estimator (LSE) of the matrix $\theta$ in an $R^d$-valued regression model $X_n = \theta^t \phi_{n-1} + \epsilon_n$, where $(\epsilon_n)$ is a generalized gaussian noise. We apply these results to study the error of the LSE for a stable $R^d$-valued linear autoregressive model of order $p$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-04-16
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/45
10.	Identifier	Digital Object Identifier	10.1214/EJP.v4-45
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 4
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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