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Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimatesстатья
- Авторы: Konakov Valentin, Panov Vladimir, Piterbarg Vladimir
- Сборник: ArXiv.org.e-Print [math.PR]
- Серия: [math.PR]
- Том: 2010
- Год издания: 2020
- Место издания: ArXiv.org.e-Print United States
- Первая страница: 1
- Последняя страница: 34
- Аннотация: In this paper, we consider the distribution of the supremum ofnon-stationary Gaussian processes, and present a new theoretical result onthe asymptotic behaviour of this distribution. Unlike previously known factsin this eld, our main theorem yields the asymptotic representation of the correspondingdistribution function with exponentially decaying remainder term.This result can be eciently used for studying the projection density estimates,based, for instance, on Legendre polynomials. More precisely, we construct thesequence of accompanying laws, which approximates the distribution of maximaldeviation of the considered estimates with polynomial rate. Moreover, weconstruct the condence bands for densities, which are honest at polynomialrate to a broad class of densities.
- Добавил в систему: Питербарг Владимир Ильич