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2019 Maximum likelihood estimation for Gaussian processes under inequality constraints
François Bachoc, Agnès Lagnoux, Andrés F. López-Lopera
Electron. J. Statist. 13(2): 2921-2969 (2019). DOI: 10.1214/19-EJS1587

Abstract

We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of the microergodic parameter of the Matérn and Wendland covariance functions. First, we show that the (unconstrained) maximum likelihood estimator has the same asymptotic distribution, unconditionally and conditionally to the fact that the Gaussian process satisfies the inequality constraints. Then, we study the recently suggested constrained maximum likelihood estimator. We show that it has the same asymptotic distribution as the (unconstrained) maximum likelihood estimator. In addition, we show in simulations that the constrained maximum likelihood estimator is generally more accurate on finite samples. Finally, we provide extensions to prediction and to noisy observations.

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François Bachoc. Agnès Lagnoux. Andrés F. López-Lopera. "Maximum likelihood estimation for Gaussian processes under inequality constraints." Electron. J. Statist. 13 (2) 2921 - 2969, 2019. https://doi.org/10.1214/19-EJS1587

Information

Received: 1 September 2018; Published: 2019
First available in Project Euclid: 3 September 2019

zbMATH: 07104734
MathSciNet: MR3998932
Digital Object Identifier: 10.1214/19-EJS1587

Subjects:
Primary: 62M30
Secondary: 62F12

JOURNAL ARTICLE
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Vol.13 • No. 2 • 2019
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