Diseños D-óptimos para modelos no lineales heteroscedásticos con información a priori
Cargando...
Autores
Director
Tipo de contenido
Document language:
Español
Fecha
Título de la revista
ISSN de la revista
Título del volumen
Documentos PDF
Resumen
Los diseños óptimos son utilizados para determinar las mejores condiciones donde se debe realizar un experimento para obtener ciertas propiedades estadísticas. En los modelos no lineales heteroscedásticos donde la varianza es una función de la media, el criterio de optimalidad depende de la elección de un valor local para los parámetros del modelo. Una forma de evitar esta dependencia es considerar una distribución a priori para el vector de parámetros del modelo e incorporarla en el criterio de optimalidad que se va a optimizar. Uno de los criterios más populares es el criterio D-optimalidad, el cual proporciona los puntos experimentales donde se minimiza el volumen del elipsoide de confianza asociado al vector de parámetros. En este trabajo se estudiaron diseños D-óptimos en modelos no lineales heteroscedásticos cuando se incorpora una distribución a priori asociada a los parámetros del modelo. Mediante la eficiencia se comparan los diseños obtenidos. Se extendió el teorema de equivalencia para incorporar el efecto de la a priori. Se muestran diferentes estructuras para la matriz de información y se consideró la familia de localización y escala con el fin de estudiar la robustez de los diseños
Abstract: Optimal design are a key tool for establishing the best condition to perform an experiment. In heteroscedastics linear and nonlinear models where variance is a power of the mean, the optimality criteria depends on the choice of a local value for the parameters. A way to avoid this dependence is by considering a prior distribution for the parameter vector and incorporate it into the optimality criteria to be optimized. One of the most popular criteria is the criterion of D-optimality, which provides the experimental points where the volume of the confidence ellipsoid associated to the parameter vector is minimized. In this paper we studied D - optimal designs in heteroscedastic nonlinear models when a distribution is incorporated a priori associated with the parameters of the model. Through efficiency the obtained designs are compared. The equivalence theorem was extended to incorporate the effect of the a priori. Different structures for the information matrix are shown and the family of location and scale is considered in order to study the robustness of the designs.
Abstract: Optimal design are a key tool for establishing the best condition to perform an experiment. In heteroscedastics linear and nonlinear models where variance is a power of the mean, the optimality criteria depends on the choice of a local value for the parameters. A way to avoid this dependence is by considering a prior distribution for the parameter vector and incorporate it into the optimality criteria to be optimized. One of the most popular criteria is the criterion of D-optimality, which provides the experimental points where the volume of the confidence ellipsoid associated to the parameter vector is minimized. In this paper we studied D - optimal designs in heteroscedastic nonlinear models when a distribution is incorporated a priori associated with the parameters of the model. Through efficiency the obtained designs are compared. The equivalence theorem was extended to incorporate the effect of the a priori. Different structures for the information matrix are shown and the family of location and scale is considered in order to study the robustness of the designs.