Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/62238 
Erscheinungsjahr: 
2000
Schriftenreihe/Nr.: 
SFB 373 Discussion Paper No. 2000,75
Verlag: 
Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin
Zusammenfassung: 
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.
Persistent Identifier der Erstveröffentlichung: 
Dokumentart: 
Working Paper

Datei(en):
Datei
Größe
317.84 kB





Publikationen in EconStor sind urheberrechtlich geschützt.