Central Limit Theorem for multiple integrals with respect to the empirical process
- Barrio, Eustasio del
- Boistard, Hélène
Publisher: Comité organizador del XXX Congreso Nacional de Estadística e Investigación Operativa y IV Jornadas de Estadística Pública
ISBN: 978-84-690-7249-3
Year of publication: 2007
Congress: Congreso Nacional de Estadística e Investigación Operativa (30. 2007. Valladolid)
Type: Conference paper
Abstract
In this talk, we will give results about weak convergence of multiple stochas- tic integrals with respect to the empirical process. We include the case in which the kernel is non degenerate with respect to the underlying distribution. Our re- sults are closely related to earlier work on U-statistics.We introduce a stochastic integral with respect to the Brownian bridge which allows us to express the limit in a uni¯ed way for both the degenerate and non degenerate cases. We also include some new results on the bootstrap of multiple integrals with respect to the empirical process.