Asymptotic equivalence of estimating a poisson intensity and a positive diffusion drift

Arbeitspapier

We consider a diffusion model of small variable type with positive drift density varying in a nonparametric set. We investigate Gaussian and Poisson approximations to this model. In the sense of asymptotic equivalence of experiments, it is shown that observation of the diffusion process until its first hitting time of level one is a natural model for the purpose of inference of the drift density. The diffusion model can be discretized by the collection of level crossing times for a uniform grid of levels. The random time increments are asymptotically sufficient and obey a nonparametric regression model with independent data. This decoupling is then used to establish asymptotic equivalence to Gaussian signal-in-white noise and Poisson intensity models on the unit interval. and also to an i.i.d. model when the diffusion drift function f is a probability density. As an application, we find the exact asymptotic minimax constant for estimating the diffusion drift density with sup-norm loss.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: SFB 373 Discussion Paper ; No. 2000,75

Klassifikation und Themen

• Klassifikation: Wirtschaft

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Genon-Catalot, Valentine ; Laredo, Catherine ; Nussbaum, Michael
• Ereignis: Veröffentlichung
• (wer): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (wo): Berlin
• (wann): 2000

Weitere Informationen

• Handle: http://hdl.handle.net/10419/62238
• URN: urn:nbn:de:kobv:11-10048015
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ