Asymptotic properties of a maximum likelihood estimator with data from a Gaussian process

Zhiliang Ying

Journal of Multivariate Analysis, 1991, vol. 36, issue 2, 280-296

Abstract: We consider an estimation problem with observations from a Gaussian process. The problem arises from a stochastic process modeling of computer experiments proposed recently by Sacks, Schiller, and Welch. By establishing various representations and approximations to the corresponding log-likelihood function, we show that the maximum likelihood estimator of the identifiable parameter [theta][sigma]2 is strongly consistent and converges weakly (when normalized by [radical sign]n) to a normal random variable, whose variance does not depend on the selection of sample points. Some extensions to regression models are also obtained.

Keywords: Ornstein-Uhlenbeck; process; maximum; likelihood; estimator; computer; experiments; consistency; asymptotic; normality; regression; model; least; squares; estimator (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (11)

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