Please use this identifier to cite or link to this item: http://hdl.handle.net/10174/36452

Title: Estimation for stochastic differential equation mixed models using approximation methods
Authors: Jamba, Nelson T.
Jacinto, Gonçalo
Filipe, Patrícia A.
Braumann, Carlos A.
Keywords: delta method
Laplace method
maximum likelihood estimation
mixed models
stochastic differential equations
Issue Date: Feb-2024
Publisher: AIMS Press
Citation: Nelson T. Jamba, Gonçalo Jacinto, Patrícia A. Filipe, Carlos A. Braumann. Estimation for stochastic differential equation mixed models using approximation methods[J]. AIMS Mathematics, 2024, 9(4): 7866-7894. doi: 10.3934/math.2024383
Abstract: We used a class of stochastic differential equations (SDE) to model the evolution of cattle weight that, by an appropriate transformation of the weight, resulted in a variant of the Ornstein-Uhlenbeck model. In previous works, we have dealt with estimation, prediction, and optimization issues for this class of models. However, to incorporate individual characteristics of the animals, the average transformed size at maturity parameter \alpha and/or the growth parameter \beta may vary randomly from animal to animal, which results in SDE mixed models. Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models.
URI: 10.3934/math.2024383 Previous ArticleNext Article
http://hdl.handle.net/10174/36452
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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