Asymptotic equivalence of estimating a Poisson intensity and a positive diffusion drift
Poisson 强度估计与正漂移扩散估计的渐近等价性
We consider a diffusion model of small variance 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 on the drift density. The diffusion model can be discretized by the collection of level crossing times…