A functional equation arising in multi-agent statistical decision theory.
A note on the Hájek-LeCam bound
Admissible invariant estimators in a linear model
Let be observation vector in the usual linear model with expectation and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic is called invariant estimator for a parametric function if its MSE depends on only through . It is shown that is admissible invariant for , if and only if, it is a BLUE of in the case when is estimable with zero variance, and it is of the form , where and is an arbitrary BLUE, otherwise. This result is used in...
Algorithmical complexity of some statistical decision processes. II
Algorithmical complexity of some statistical decision processes. I
Algunos progresos y problemas en la Ciencia de la decisión.
The study of decision making and problem solving has attracted much attention. Since the middle of this century the notion of rational decision making was associated with expected utility maximization, albeit in a very different way than D. Bernoulli (1738) envisioned. For decisions under risk, Von Neumann and Morgenstern (1947) formulated the axioms for expected utility. For decisions under uncertainty Savage (1954) developed the axioms leading simultaneously to subjective probability and expected...
Criterion of maximizing the expected quietness (invariant by homotethies in relation to the utilities)
Criterios de selección de reglas de decisión con observaciones continuas.
Decision analysis via granulation based on general binary relation.
Decisión equivariante óptima en poblaciones con parámetro de localización y escala.
En este trabajo se trata el problema de decisión equivariante en poblaciones dependientes de un parámetro bidimensional del tipo de localización y escala, obteniendo la información a partir de un estadístico ordenado. Tras caracterizar las funciones de decisión equivariantes y encontrar la expresión para la función de decisión óptima, se ven condiciones, sobre la función de pérdida y distribución muestral, que sean suficientes para garantizar que la función de decisión equivariante óptima sea minimax...
Decision Theory Based on Non-Additive Measures
Equivalencia de problemas de decisión.
En este trabajo se introduce una definición de equivalencia de problemas de decisión. Los resultados y ejemplos que presentamos muestran que esta definición de equivalencia se adapta bien a la metodología de la estadística.
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.
Further evidence against independence preservation in expert judgement synthesis.
Generalized regression estimation for continuous time processes with values in functional spaces
We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the...
Invariance and R-ε criterion.
The R-ε criterion is considered as a generalization of the minimax criterion, in a decision problem with Θ = {θ1, ..., θn}, and its relation with the invariance is studied. If a decision problem is invariant under a finite group G, it is known, from the minimax point of view that, for any rule δ, there exists an invariant rule δ' which is either preferred or equivalent to δ. The question raised in this paper is: given that the minimax ordering is a particular case of R-ε ordering, is it possible...
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.
Les -values comme votes d’experts
Les P-values comme votes d'experts
The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the two-sided hypothesis problem. We analyze this practice with a new approach to statistical inference. First we select good decision rules without using a loss function, we call them experts. Then we define a probability distribution on the space...
On a robust significance test for the Cox regression model
A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.