Maximum likelihood estimation for Gaussian processes under inequality constraints

Abstract : We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We first 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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01864340
Contributeur : Andrés Lopez-Lopera <>
Soumis le : mercredi 29 août 2018 - 16:50:14
Dernière modification le : mardi 19 mars 2019 - 01:19:04

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  • HAL Id : hal-01864340, version 1
  • ARXIV : 1804.03378

Citation

François Bachoc, Agnes Lagnoux, Andrés F. López-Lopera. Maximum likelihood estimation for Gaussian processes under inequality constraints. 2018. 〈hal-01864340〉

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