Equivalence Theory for Density Estimation, Poisson Processes and Gaussian White Noise With Drift
نویسندگان
چکیده
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models.
منابع مشابه
Equivalence Theory for Density Estimation, Poisson Processes and Gaussian White Noise with Drift by Lawrence
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic e...
متن کاملAsymptotic Equivalence of Spectral Density Estimation and Gaussian White Noise by Georgi
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam’s deficiency -distance, to two Gaussian experiments with simpler structure is established. The first one is given by independent zero mean Gaussians with variance approximately f (ωi), where ωi is ...
متن کاملAsymptotic Equivalence of Estimating a Poisson Intensity and a Positive Diffusion Drift by Valentine Genon-catalot,
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...
متن کاملAsymptotic Equivalence of Spectral Density Estimation and Gaussian White Noise
We consider the statistical experiment given by a sample y(1), . . . , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam’s deficiency ∆-distance, to two Gaussian experiments with simpler structure is established. The first one is given by independent zero mean Gaussians with variance approximately f(ωi) where ωi is a...
متن کاملConstructive Asymptotic Equivalence of Density Estimation and Gaussian White Noise
A recipe is provided for producing, from a sequence of procedures in the Gaus-sian regression model, an asymptotically equivalent sequence in the density estimation model with i. i. d. observations. The recipe is, to put it roughly, to calculate normalised frequencies over certain intervals, add a small random distortion, calculate square roots, and pretend these to be observations from a Gauss...
متن کامل