文章基本信息

标题：Maximum likelihood estimation for Gaussian processes under inequality constraints
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作者：François Bachoc ; Agnès Lagnoux ; Andrés F. López-Lopera 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：2921-2969
DOI：10.1214/19-EJS1587
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Gaussian processes; inequality constraints; fixed-domain asymptotics; constrained maximum likelihood; asymptotic normality