A CLT for empirical processes involving time-dependent data

• Autores: James Kuelbs, Thomas G. Kurtz, Joel Zinn
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 2, 2013, págs. 785-816
• Idioma: inglés
• DOI: 10.1214/11-AOP711
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• Resumen

  • For stochastic processes {Xt : t∈E}, we establish sufficient conditions for the empirical process based on {IXt≤y−Pr(Xt≤y) : t∈E,y∈R} to satisfy the CLT uniformly in t∈E, y∈R. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and E=[0,1].