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

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.

Detection, modelling and estimation of non-linear trends by using a non-homogeneous Vasicek stochastic diffusion. Application to CO2 emissions in Morocco

“…Moreover, this idea for making the baseline diffusion non-homogeneous may also be applied simultaneously to the diffusion coefficient, such that the latter, too, becomes non homogeneous. This approach has been developed in certain specific diffusion models implemented in various scientific fields (see, for example, Gutiérrez et al 1999Gutiérrez et al , 2008b and also in lognormal and Gompertz diffusion random fields, see Gutiérrez et al (2007b) and Gutiérrez (2010). In the present study, we shall apply this methodology to the Vasicek case.…”