A0318
Title: Maximum likelihood estimation for Gaussian processes under inequality constraints
Authors: Francois Bachoc - Universite Paul Sabatier (France) [presenting]
Abstract: Covariance parameter estimation is considered for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotic. The estimation of the variance parameter and the estimation of the micro ergodic parameter of the Matern and Wendland covariance functions are addressed. First, it is shown 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, the recently suggested constrained maximum likelihood estimator is studied. It is shown that it has the same asymptotic distribution as the (unconstrained) maximum likelihood estimator. In addition, it is shown in simulations that the constrained maximum likelihood estimator is generally more accurate on finite samples.
