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-01772560
Contributeur : François Bachoc <>
Soumis le : vendredi 20 avril 2018 - 13:44:53
Dernière modification le : samedi 27 octobre 2018 - 01:29:42

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  • HAL Id : hal-01772560, version 1
  • ARXIV : 1804.03378

Citation

François Bachoc, Agnès Lagnoux, Andrés F. López-Lopera. Maximum likelihood estimation for Gaussian processes under inequality constraints. 2018. 〈hal-01772560〉

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