The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.
The problem considered is that of estimation of the size (N) of a closed population under three sampling schemes admitting unbiased estimation of N. It is proved that for each of these schemes, the uniformly minimum variance unbiased estimator (UMVUE) of N is inadmissible under square error loss function. For the first scheme, the UMVUE is also the maximum likelihood estimator (MLE) of N. For the second scheme and a special case of the third, it is shown respectively that an MLE and an estimator...
En este trabajo se propone y estudia una medida para la incertidumbre correspondiente a las utilidades, o inquietud. Este concepto recibe por vez primera un tratamiento matemático. En la etapa inicial del trabajo se consideran conjuntos constituidos por resultados elementales, y en una segunda etapa se consideran conjuntos constituidos por pares de resultados.
En este trabajo consideramos el problema de la evaluación multiatributo en términos de una función de valor vectorial que conduce a un espacio de criterios en el que suponemos es posible obtener información parcial secuencial sobre las preferencias la cual se traduce en conos definidos sobre el espacio de criterios. También consideramos dentro del esquema señalado la situación en la cual el decisor parte de un subconjunto del conjunto total de decisiones, introduciendo el conjunto K-eficiente aproximado...
We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let be a class of functions on the parameter space and consider estimating elements of under quadratic loss. If the formal Bayes estimator of every function in is admissible, then the prior is strongly admissible with respect to . Eaton’s method for establishing strong admissibility is based on studying the stability properties of a particular Markov chain associated with the inferential...
R-ε criterion is considered in a decision problem (Θ, D*, R). Some considerations are made for the case in which the parameter space Θ is finite. Finally the existence of a decision rule with the minimum R-ε risk is examined, when the risk set is closed from below and bounded.
For a sequence of statistical experiments with a finite parameter set the asymptotic behavior of the maximum risk is studied for the problem of classification into disjoint subsets. The exponential rates of the optimal decision rule is determined and expressed in terms of the normalized limit of moment generating functions of likelihood ratios. Necessary and sufficient conditions for the existence of adaptive classification rules in the sense of Rukhin [Ru1] are given. The results are applied to...
We consider a Wright-Fisher diffusion (x(t)) whose current state cannot be observed directly. Instead, at times t1 < t2 < ..., the observations y(ti) are such that, given the process (x(t)), the random variables (y(ti)) are independent and the conditional distribution of y(ti) only depends on x(ti). When this conditional distribution has a specific form, we prove that the model ((x(ti),y(ti)), i≥1) is a computable filter in the sense that all distributions involved in filtering, prediction...
Este trabajo contiene la definición, justificación intuitiva, caracterización y principales propiedades y casos particulares de las denominadas funciones de evaluación modales. Se considera un problema de decisión con espacio paramétrico finito y conjunto de acciones igual al conjunto de posibles distribuciones de probabilidad sobre él; se trata de estudiar las funciones de utilidad que, en este caso y mediante el criterio Bayes, conducen a tomar como acción óptima la distribución degenerada en...
Let Y be a random vector taking its values in a measurable space and let z be a vector-valued function defined on that space. We consider gamma minimax estimation of the unknown expected value p of the random vector z(Y). We assume a weighted squared error loss function.