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Towards a notion of testability

Czesław Stępniak (1992)

Applications of Mathematics

The problem of testability has been undertaken many times in the context of linear hypotheses. Almost all these considerations restricted to some algebraical conditions without reaching the nature of the problem. Therefore, a general and commonly acceptable notion of testability is still wanted. Our notion is based on a simple and natural decision theoretic requirement and is characterized in terms of the families of distributions corresponding to the null and the alternative hypothesis. Its consequences...

Two-point priors and minimax estimation of a bounded parameter under convex loss

Agata Boratyńska (2005)

Applicationes Mathematicae

The problem of minimax estimation of a parameter θ when θ is restricted to a finite interval [θ₀,θ₀+m] is studied. The case of a convex loss function is considered. Sufficient conditions for existence of a minimax estimator which is a Bayes estimator with respect to a prior concentrated in two points θ₀ and θ₀+m are obtained. An example is presented.

Una aplicación de la teoría de la utilidad de Von Neumann a la probabilidad subjetiva.

Enrique Caro (1985)

Trabajos de Estadística e Investigación Operativa

En este artículo se da una condición necesaria y suficiente para la existencia y unicidad de una probabilidad subjetiva, finitamente aditiva, que concuerda con una probabilidad comparativa definida en una cierta clase de sucesos asociada al espacio paramétrico objeto de la inferencia.Nuestra constribución no evita tener que postular la relación de probabilidad comparativa en una clase mayor que la que es objeto de nuestro estudio pues exige la introducción de un espacio auxiliar que es el intervalo...

Una clase de problemas de decisión bajo incertidumbre parcial.

Manuel Salvador Figueras (1989)

Trabajos de Investigación Operativa

Se estudia el Problema de Decisión cuando el ambiente es de incertidumbre parcial, en el sentido de que la distribución a priori -que se supone absolutamente continua- sobre el espacio de estados -un intervalo real- no se conoce en su totalidad, sino que tan sólo se posee información respecto a las probabilidades de algunos subintervalos de Θ o acotaciones de éstas, así como algunas restricciones sobre los momentos y ciertas generalizaciones de éstas, dentro de este contexto.Además de las correspondientes...

Unbiased estimation of reliability for two-parameter exponential distribution under time censored sampling

S. Sengupta (2010)

Applicationes Mathematicae

The problem considered is that of unbiased estimation of reliability for a two-parameter exponential distribution under time censored sampling. We give necessary and sufficient conditions for the existence of uniformly minimum variance unbiased estimator and also provide a characterization of a complete class of unbiased estimators in situations where unbiased estimators exist.

Weak Consistency: A New Approach to Consistency in the Saaty’s Analytic Hierarchy Process

Věra Jandová, Jana Talašová (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the decision making methods based on the pairwise comparison there is very important to enter the preferences of compared elements in the rational way. Only in this case we are able to obtain the reasonable solution. In the Analytic Hierarchy Process (AHP) there is set a strict consistency condition in order to keep the rationality of preference intensities between compared elements. But this requirement for the Saaty’s matrix is not achievable in the real situations because of the Saaty’s scale...

Why minimax is not that pessimistic

Aurelia Fraysse (2013)

ESAIM: Probability and Statistics

In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...

Γ-minimax sequential estimation for Markov-additive processes

Ryszard Magiera (2001)

Applicationes Mathematicae

The problem of estimating unknown parameters of Markov-additive processes from data observed up to a random stopping time is considered. To the problem of estimation, the intermediate approach between the Bayes and the minimax principle is applied in which it is assumed that a vague prior information on the distribution of the unknown parameters is available. The loss in estimating is assumed to consist of the error of estimation (defined by a weighted squared loss function) as well as a cost of...

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