Electronic Journal of Probability

Moderate deviations for stable Markov chains and regression models

Julien Worms

Full-text: Open access

Abstract

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 $p$.

Article information

Source
Electron. J. Probab., Volume 4 (1999), paper no. 8, 28 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1457125517

Digital Object Identifier
doi:10.1214/EJP.v4-45

Mathematical Reviews number (MathSciNet)
MR1684149

Zentralblatt MATH identifier
0980.62082

Subjects
Primary: 60F10: Large deviations
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 62J05: Linear regression 62J02: General nonlinear regression

Keywords
Large and Moderate Deviations Martingales Markov Chains Least Squares Estimator for a regression model

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Worms, Julien. Moderate deviations for stable Markov chains and regression models. Electron. J. Probab. 4 (1999), paper no. 8, 28 pp. doi:10.1214/EJP.v4-45. https://projecteuclid.org/euclid.ejp/1457125517


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