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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


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.


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

Primary: 62M30
Secondary: 62F12

Keywords: asymptotic normality , constrained maximum likelihood , fixed-domain asymptotics , Gaussian processes , inequality constraints


Vol.13 • No. 2 • 2019
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