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Moderate deviations for stable Markov chains and regression models

   
@article{EJP45,
	author = {Julien Worms},
	title = {Moderate deviations for stable Markov chains and regression models},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {4},
	year = {1999},
	keywords = {Large and Moderate Deviations, Martingales, Markov Chains,  Least Squares Estimator for a regression model.},
	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 $p$.},
	pages = {no. 8, 1-28},
	issn = {1083-6489},
	doi = {10.1214/EJP.v4-45},    
        url = {http://ejp.ejpecp.org/article/view/45}}