Name
Abstract | ||
|---|---|---|
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 h0 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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jmva.2008.10.004 | J. Multivariate Analysis |
Keywords | Field | DocType |
legendre polynomial,gumbel distribution,stochastic integral,secondary,gumbel distri- bution,62j12,and phrases: extreme value asymptotics,brownian motion,main result,limit distribution,polynomial regression model,polynomial regression,primary,legendre polynomials,gaussian processes,quasi-likelihood procedure,global near-surface temperature,extreme value asymptotics,limit result,60g70,62j02,extreme value theory,exact tail behavior,extremal behavior,standard deviation,extreme value,gaussian process | Mathematical analysis,Extreme value theory,Polynomial regression,Infimum and supremum,Gumbel distribution,Legendre polynomials,Gaussian process,Statistics,Brownian motion,Mathematics,Asymptotic distribution | Journal |
Volume | Issue | ISSN |
100 | 5 | Journal of Multivariate Analysis |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Aue | 1 | 6 | 2.86 |
| Lajos Horváth | 2 | 28 | 9.10 |
| Marie Hušková | 3 | 23 | 9.73 |