Parametric nonstationary correlation models

Jacqueline M. Hughes-Oliver, Graciela Gonzalez-Farias, Jye-Chyi Lu and Di Chen

Statistics & Probability Letters, 1998, vol. 40, issue 3, 267-278

Abstract: Stochastic processes observed over space often exhibit nonstationarity. Possible causes of nonstationarity include mean drift, heterogeneity of responses, or a correlation pattern that is not simply a function of the Euclidean distance between two spatial locations. This paper considers the latter. The need for nonstationary correlation models has been demonstrated in several application areas, including environmental monitoring of pollutants, and modeling of semiconductor fabrication processes. We present parametric nonstationary correlation models for capturing the effect of point sources. For example, if the response variable is carbon monoxide, then a smoke stack producing carbon monoxide would be considered a point source, and it is unreasonable to believe that correlation would not depend on proximity to the smoke stack. Our parametric models allow the consideration of multiple-point sources, as well as testing the strength of a particular source. These models have the usual anisotropic and isotropic exponential correlation functions as special cases.

Keywords: Anisotropy; Point; source; Pollution; monitoring; Positive; semidefinite; kernel; Positive; semidefinite; matrix; Semi-conductor; fabrication (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (4)

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