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Abstract Filipe+Braumann WNI 2008

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A SDE growth model: Nonparametric Estimation of the Drift and the Diffusion Coefficients

Patr´ıcia A. Filipe, CIMA - Universidade de ´Evora [email protected]

Carlos A. Braumann, CIMA - Universidade de ´Evora [email protected]

Abstract: We study a stochastic differential equation (SDE) growth model to describe individual growth in random environments. In particular, in this work, we discuss the estimation of the drift and the diffusion coefficients us- ing non-parametric methods. We illustrate the methodology by using bovine growth data.

Considering the diffusion processXt, describing the weight of an animal at aget, characterized by the stochastic differential equationdXt=a(Xt)dt+ b(Xt)dWt, with Wt being the Wiener process, we estimate the infinitesi- mal coefficients a(x) and b(x) nonparametrically. Our goal was to analyse which of the parametric models (with specific functional forms fora(x) and b(x)) previously used by us to describe the evolution of bovine weight were good choices and also to see whether some alternative specific parametrized functional forms ofa(x) andb(x) might be suggested for further parametric analysis of this data.

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