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Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed.
This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants.
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We study estimation problems for periodically correlated, non gaussian processes. We estimate the correlation functions and the spectral densities from continuous-time samples. From a random time sample, we construct three types of estimators for the spectral densities and we prove their consistency.
Se centra el estudio en los problemas de control estocástico con información incompleta de parámetro discreto.Se define para estos problemas un parámetro suficiente para el proceso básico y se demuestra que la clase de controles basados en éste es esencialmente completa.Como caso particular se estudia el modelo lineal normal y se ve la relación que existe entre el proceso suficiente definido para este modelo y el filtro de Kalman.
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