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.
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https://hal.archives-ouvertes.fr/hal-01772560
Contributor : François Bachoc <>
Submitted on : Friday, April 20, 2018 - 1:44:53 PM
Last modification on : Friday, April 12, 2019 - 4:22:51 PM

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

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

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