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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-01864340
Contributor : Andrés LOPEZ LOPERA Connect in order to contact the contributor
Submitted on : Wednesday, August 29, 2018 - 4:50:14 PM
Last modification on : Monday, July 4, 2022 - 10:29:51 AM

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François Bachoc, Agnes Lagnoux, Andrés F. López-Lopera. Maximum likelihood estimation for Gaussian processes under inequality constraints. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2019, 13 (2), pp.2921-2969. ⟨10.1214/19-EJS1587⟩. ⟨hal-01864340⟩

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