Asymptotic equivalence of density estimation and Gaussian white noise
نویسندگان
چکیده
منابع مشابه
Asymptotic Equivalence of Density Estimation and Gaussian White Noise
Signal recovery in Gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation, having all the essential traits in a pure form. The equivalence has mostly been stated informally, but an approximation in the sense of Le Cam’s deficiency distance 1 would make it precise. The models are then asymptotically equivalent for ...
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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...
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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...
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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 ...
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The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time T , with T tending to ∞. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Lévy ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1996
ISSN: 0090-5364
DOI: 10.1214/aos/1032181160