Pointwise consistency of the kriging predictor with known mean and covariance functions

Emmanuel Vazquez (1, 2) , Julien Bect (1)

1 E3S - Supélec Sciences des Systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Emmanuel Vazquez, Julien Bect. Pointwise consistency of the kriging predictor with known mean and covariance functions. 9th International Workshop in Model-Oriented Design and Analysis, Jun 2010, Bertinoro, Italy. pp.221-228, ⟨10.1007/978-3-7908-2410-0⟩. ⟨hal-00440827⟩