Electronic Journal of Statistics

Maximum likelihood estimation for Gaussian processes under inequality constraints

François Bachoc, Agnès Lagnoux, and Andrés F. López-Lopera

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 2 (2019), 2921-2969.

Dates
Received: September 2018
First available in Project Euclid: 3 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1567497627

Digital Object Identifier
doi:10.1214/19-EJS1587

Mathematical Reviews number (MathSciNet)
MR3998932

Zentralblatt MATH identifier
07104734

Subjects
Primary: 62M30: Spatial processes
Secondary: 62F12: Asymptotic properties of estimators

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bachoc, François; Lagnoux, Agnès; López-Lopera, Andrés F. Maximum likelihood estimation for Gaussian processes under inequality constraints. Electron. J. Statist. 13 (2019), no. 2, 2921--2969. doi:10.1214/19-EJS1587. https://projecteuclid.org/euclid.ejs/1567497627


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