Large Toeplitz operators and quadratic form generated by stationary Gaussian sequence.
Solev, V.N., Gerville-Reache, L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Solev, V.N., Gerville-Reache, L. (2005)
Zapiski Nauchnykh Seminarov POMI
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Perrin, O., Zani, M. (2005)
Zapiski Nauchnykh Seminarov POMI
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Waclaw Timoszyk (1974)
Colloquium Mathematicae
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Bernard Bercu, Fabrice Gamboa, Marc Lavielle (2000)
ESAIM: Probability and Statistics
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Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Nicolas Privault, Anthony Réveillac (2011)
ESAIM: Probability and Statistics
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Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Michel J. G. Weber (2012)
Colloquium Mathematicae
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We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences...
J. Soler (1980)
Banach Center Publications
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S. Valère Bitseki Penda, Hacène Djellout, Frédéric Proïa (2014)
ESAIM: Probability and Statistics
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The purpose of this paper is to investigate moderate deviations for the Durbin–Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate...