Extreme value theory for stochastic integrals of Legendre polynomials
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- 作者：Alex ; er Aue ; Lajos Horvá ; th ; Marie Huš ; ková
- 关键词：Extreme value asymptotics ; Gaussian processes ; Gumbel distribution ; Legendre polynomials ; Polynomial regression
- 刊名：Journal of Multivariate Analysis
- 出版年：2009
- 出版时间：May 2009
- 年：2009
- 卷：100
- 期：5
- 页码：1029-1043
- 全文大小：1070 K
文摘
We study in this paper the extremal behavior of stochastic integrals of Legendre polynomial transforms with respect to Brownian motion. As the main results, we obtain the exact tail behavior of the supremum of these integrals taken over intervals [0,h] with h>0 fixed, and the limiting distribution of the supremum on intervals [0,T] as T→∞. We show further how this limit distribution is connected to the asymptotic of the maximally selected quasi-likelihood procedure that is used to detect changes at an unknown time in polynomial regression models. In an application to global near-surface temperatures, we demonstrate that the limit results presented in this paper perform well for real data sets.