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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2006

Moderate deviations of empirical periodogram and non-linear functionals of moving average processes.

Résumé

A moderate deviation principle for nonlinear functionals, with at most quadratic growth, of moving average processes (or linear processes) is established. The main assumptions on the moving average process are a logarithmic Sobolev inequality for the driving random variables and the continuity, or some (weaker) integrability condition on the spectral density (covering some cases of long-range dependence). We also obtain the moderate deviation estimate for the empirical periodogram, exhibiting an interesting new form of the rate function, i.e. with a correction term compared to the Gaussian rate functional. As statistical applications we provide the moderate deviation estimates of the least-square and the Yule-Walker estimators of the parameter of a stationary autoregressive process and of the Neyman-Pearson likelihood ratio test in the Gaussian case.
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hal-00469713 , version 1 (02-04-2010)

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  • HAL Id : hal-00469713 , version 1

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Hacène Djellout, Arnaud Guillin, Liming Wu. Moderate deviations of empirical periodogram and non-linear functionals of moving average processes.. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2006, 42 (4), pp.393--416. ⟨hal-00469713⟩
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