Central Limit Theorem for multiple integrals with respect to the empirical process

  1. Barrio, Eustasio del
  2. Boistard, Hélène
Llibre:
XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública: actas

Editorial: Comité organizador del XXX Congreso Nacional de Estadística e Investigación Operativa y IV Jornadas de Estadística Pública

ISBN: 978-84-690-7249-3

Any de publicació: 2007

Congrés: Congreso Nacional de Estadística e Investigación Operativa (30. 2007. Valladolid)

Tipus: Aportació congrés

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Resum

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.

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