Asymptotic equivalence of spectral density estimation and gaussian white noise

By G. Golubev, Michael Nussbaum, Harrison H. Zhou. 2009

54 citations recorded by the source corpus.

We 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c4bf904d0c130a857f0e0fe894e517817f492510

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Citations in the corpus

Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “This structure was originally considered in Johnstone (2001) and have been studied by several papers under the sparse principal component analysis setting, including Paul (2007), Nadler (2008), Johnstone and Lu (2009), Amini andWainwright (2009), Birnbaum et al.”