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

  • R. Gutiérrez
  • C. Roldán
  • R. Gutiérrez-Sánchez
  • J. M. Angulo
Original Paper

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 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • R. Gutiérrez
    • 1
  • C. Roldán
    • 2
  • R. Gutiérrez-Sánchez
    • 1
  • J. M. Angulo
    • 1
  1. 1.Department of Statistics and Operations ResearchUniversity of GranadaGranadaSpain
  2. 2.Department of Statistics and Operations ResearchUniversity of JaénJaénSpain

Personalised recommendations