Original Paper

Stochastic Environmental Research and Risk Assessment

, Volume 24, Issue 4, pp 539-546

First online:

The effect of nested grid sampling on the parameter estimation of a spatial Gompertz diffusion

  • R. GutiérrezAffiliated withDepartment of Statistics and Operations Research, University of Granada
  • , C. RoldánAffiliated withDepartment of Statistics and Operations Research, University of Jaén Email author 
  • , R. Gutiérrez-SánchezAffiliated withDepartment of Statistics and Operations Research, University of Granada
  • , J. M. AnguloAffiliated withDepartment of Statistics and Operations Research, University of Granada

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

This paper evaluates the effects of using data observed on regular nested grids on the parameter estimates of a two-parameter Gompertz diffusion model. This new spatial diffusion process represents a technically more complex stage of Gompertz modeling. Firstly, the diffusion model is introduced through an appropriate transformation of a two-parameter Gaussian diffusion process. Probabilistic characteristics of this model, such as the transition densities and the trend functions, are obtained. Secondly, statistical estimation is considered using data obtained on a regular or irregular grid; the explicit expression of the likelihood equations and the parameter estimators are given for regular grids. Finally, a simulation experiment illustrates the results of this paper.

Keywords

Diffusion process Gompertz diffusion process Maximum likelihood Spatial process