Open Access
1999 Moderate deviations for stable Markov chains and regression models
Julien Worms
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Electron. J. Probab. 4: 1-28 (1999). DOI: 10.1214/EJP.v4-45


We prove moderate deviations principles for:

  • 1. 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 $(r,s)$;

  • 2. 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 $p$.


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Julien Worms. "Moderate deviations for stable Markov chains and regression models." Electron. J. Probab. 4 1 - 28, 1999.


Accepted: 16 April 1999; Published: 1999
First available in Project Euclid: 4 March 2016

zbMATH: 0980.62082
MathSciNet: MR1684149
Digital Object Identifier: 10.1214/EJP.v4-45

Primary: 60F10
Secondary: 60J10 , 62J02 , 62J05

Keywords: large and moderate deviations , Least Squares Estimator for a regression model , Markov chains , Martingales

Vol.4 • 1999
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