Geostatistical Modeling via Karhunen-Loeve Expansion

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Tingjin Chu*+
• Companies: Renmin University of China
• Keywords: geostatistical models ; spatial/spatio-temporal process ; Gaussian process ; likelihood-based functions ; functional data algorithms

Abstract

Geostatistical data is collected and used in many areas and geostatistical models are useful tools to investigate these data. For accurate model estimation and prediction, spatial/spatio-temporal correlation needs to be incorporated in the model and estimated properly.

In this paper, spatial/spatio-temporal correlation is represented by an underlying spatial/spatio-temporal process, which is assumed to be a Gaussian process. It is well-known that Gaussian process can be represented by Karhunen-Loeve expansions. Moreover, Karhunen-Loeve expansion does not assume the form of the covariance structure, and therefore, the covariance structure of spatial/spatio-temporal process is more flexible. For example, isotropy assumption is not needed in this approach. The geostatistical modeling is then estimated through likelihood-based functions to ensure consistency and asymptotic normality of parameter estimation. In this algorithm, the estimation of spatial/spatio-temporal processes can be carried out by existing functional data algorithms, which is fast to compute. For the proposed methods, theoretical results are established. Moreover, simulation studies are conducted to show the perform