Gaussian Subordination Models on a Lattice with Environmental Applications

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Sucharita Ghosh*+
• Companies: Swiss Federal Research Institute WSL
• Keywords: Spatial data ; Smoothing ; Long-range dependence ; Large deviation ; Forestry ; Ecology

Abstract

Suppose that spatial observations Y(i,j) occur on a lattice (i,j), i= 1,...,n, j=1,2,.,m such that the data are Gaussian subordinated via a function G that is unknown and arbitrary except that it allows for a Hermite polynomial expansion. The advantage of this model is that it allows for non-Gaussianity of the data and that the shape of the underlying probability distribution may be location dependent. We consider various correlation types and in particular short memory and long-memory correlations and address two topics: (a) the nonparametric regression problem where the errors are Gaussian subordinated as described above and (b) the species count problem where the background process that is decisive of species occurrence is a Gaussian subordinated process. Generalization to the case when the data are irregularly spaced in space are also considered. We discuss asymptotic results and some real data applications from environmental monitoring.