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Maximum likelihood estimation and prediction error for a Matérn model on the circle

Abstract : This work considers Gaussian process interpolation with a periodized version of the Matérn covariance function (Stein, 1999, Section 6.7) with Fourier coefficients φ(α^2 + j^2)^(−ν−1/2). Convergence rates are studied for the joint maximum likelihood estimation of ν and φ when the data is sampled according to the model. The mean integrated squared error is also analyzed with fixed and estimated parameters, showing that maximum likelihood estimation yields asymptotically the same error as if the ground truth was known. Finally, the case where the observed function is a "deterministic" element of a continuous Sobolev space is also considered, suggesting that bounding assumptions on some parameters can lead to different estimates.
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Preprints, Working Papers, ...
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03778527
Contributor : Sébastien Petit Connect in order to contact the contributor
Submitted on : Thursday, September 15, 2022 - 9:33:47 PM
Last modification on : Saturday, September 17, 2022 - 3:25:21 AM

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  • HAL Id : hal-03778527, version 1
  • ARXIV : 2209.07791

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Sébastien Petit. Maximum likelihood estimation and prediction error for a Matérn model on the circle. 2022. ⟨hal-03778527⟩

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