Asymptotic equivalence of spectral density estimation and gaussian white noise

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dc.creatorGolubev, Georgi K.
dc.creatorNussbaum, Michael
dc.creatorZhou, Harrison H.
dc.date2009-03-07
dc.date.accessioned2026-07-07T12:50:16Z
dc.date.available2026-07-07T12:50:16Z
dc.descriptionWe consider the statistical experiment given by a sample of a stationary Gaussian process with an unknown smooth spectral density f. Asymptotic equivalence, in the sense of Le Cam's deficiency Delta-distance, to two Gaussian experiments with simpler structure is established. The first one is given by independent zero mean Gaussians with variance approximately the value of f in points of a uniform grid (nonparametric Gaussian scale regression). This approximation is closely related to well-known asymptotic independence results for the periodogram and corresponding inference methods. The second asymptotic equivalence is to a Gaussian white noise model where the drift function is the log-spectral density. This represents the step from a Gaussian scale model to a location model, and also has a counterpart in established inference methods, i.e. log-periodogram regression. The problem of simple explicit equivalence maps (Markov kernels), allowing to directly carry over inference, appears in this context but is not solved here.
dc.description39 pages
dc.identifierhttps://arxiv.org/abs/0903.1314
dc.identifierhttp://arxiv.org/abs/0903.1314
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222636
dc.subjectStatistics Theory
dc.titleAsymptotic equivalence of spectral density estimation and gaussian white noise
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