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Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimatesстатья
- Авторы: Konakov V., Panov V., Piterbarg V.
- Журнал: Extremes
- Том: 24
- Год издания: 2021
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- Первая страница: 617
- Последняя страница: 651
- DOI: 10.1007/s10687-020-00402-2
- Аннотация: We consider the distribution of the supremum ofnon-stationary Gaussian processes, and present a new theoretical result on the asymptotic behavior of this distribution. Unlike previously known factsin this eld, our main theorem yields the asymptotic representation of the corresponding distribution function with exponentially decaying remainder term. This result can be used for studying the projection density estimates, based, for instance, on Legendre polynomials. More precisely, we construct the sequence of accompanying laws, which approximates the distribution of maximal deviation of the considered estimates with polynomial rate. Moreover, we construct the confidence bands for densities, which are honest at polynomial rate to a broad class of densities.
- Добавил в систему: Питербарг Владимир Ильич