Estimation and experimental design in a linear regression model using prior information
Estimation of the scale parameter of gamma model in the presence of outlier observations.
Existencia de reglas de decisión con mínimo riesgo R-ε.
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.
Filtering the Wright-Fisher diffusion
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...
Funciones de evaluación modales.
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...
Fuzzified Blackwell's method to compare experiments
Gamma-minimax estimators for the parameters of a multinomial distribution
Generalized information criteria for Bayes decisions
This paper deals with Bayesian models given by statistical experiments and standard loss functions. Bayes probability of error and Bayes risk are estimated by means of classical and generalized information criteria applicable to the experiment. The accuracy of the estimation is studied. Among the information criteria studied in the paper is the class of posterior power entropies which include the Shannon entropy as special case for the power . It is shown that the most accurate estimate is in this...
Graphical models for hierarchical computations in the analysis and design of replications.
How powerful are data driven score tests for uniformity
We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative, in the Gaussian...
Invariancia de las reglas admisibles y Bayes respecto de transformaciones monótonas.
From an optimality point of view the solution of a decision problem is related to classes of optimal strategies: admissible, Bayes, etc. which are closely related to boundaries of the risk set S such as lower-boundary, Bayes boundary, positive Bayes boundary. In this paper we present some results concerning invariance properties of such boundaries when the set is transformed by means of a continuous monotonic increasing function W.
Invited paper with discussion: Natural Induction: An objective Bayesian approach.
Las f*-divergencias como criterio bayesiano de comparación de experimentos.
In this paper a bayesian criterion for comparing different experiments based on the maximization of the f*-Divergence is proposed and studied. After a general setting of the criterion, we prove that this criterion verifies the main properties that a criterion for comparing experiments must satisfy.
Las medidas de f*-divergencia en el diseño secuencial de experimentos en un contexto bayesiano.
Se presenta un método de selección secuencial de un número fijo de experimentos a partir de las medidas de f*-divergencia introducidas por Csiszar (1967). Este trabajo es similar al desarrollado por De Groot (1970) con funciones de incertidumbre; sin embargo, no sólo se considera el problema de espacio paramétrico finito, sino que se estudia además el caso de espacio paramétrico infinito.
Le modèle bayésien
Limits of Bayesian decision related quantities of binomial asset price models
We study Bayesian decision making based on observations () of the discrete-time price dynamics of a financial asset, when the hypothesis a special -period binomial model and the alternative is a different -period binomial model. As the observation gaps tend to zero (i. e. ), we obtain the limits of the corresponding Bayes risk as well as of the related Hellinger integrals and power divergences. Furthermore, we also give an example for the “non-commutativity” between Bayesian statistical and...
Méthodes de segmentation non paramétriques
Minimax and Bayes estimation when the loss function is unknown
Minimax Estimation for the Bounded Mean of a Bivariate Normal Distribution.
Minimax prediction of the difference of multinomial random variables