Asymptotic equivalence of spectral density and regression estimation
نویسنده
چکیده
We consider the statistical experiment given by a sample y(1); : : : ; y(n) of a stationary Gaussian process with an unknown smooth spectral density. Asymptotic equivalence with a nonparametric regression in discrete Gaussian white noise is established. The key is a local limit theorem for an increasing number of empirical covariance coe cients.
منابع مشابه
Asymptotic 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...
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