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

• Autores: Eustasio del Barrio , Hélène Boistard
• Localización: XXX Congreso Nacional de Estadística e Investigación Operativa y de las IV Jornadas de Estadística Pública: actas, 2007, ISBN 978-84-690-7249-3
• Idioma: inglés
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• Resumen

  • 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.