Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors
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Lognormal diffusion processExogenous factorsGrowth curvesMaximum likelihood estimationAsymptotic distribution
Román Román, P.; Serrano-Pérez, J.J.; Torres Ruiz, F.A. Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors. Mathematics 2018, 6, 85; doi:10.3390/math6050085.
SponsorshipThis work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grants MTM2014-58061-P and MTM2017-85568-P.
Different versions of the lognormal diffusion process with exogenous factors have been used in recent years to model and study the behavior of phenomena following a given growth curve. In each case considered, the estimation of the model has been addressed, generally by maximum likelihood (ML), as has been the study of several characteristics associated with the type of curve considered. For this process, a unified version of the ML estimation problem is presented, including how to obtain estimation errors and asymptotic confidence intervals for parametric functions when no explicit expression is available for the estimators of the parameters of the model. The Gompertz-type diffusion process is used here to illustrate the application of the methodology.