The problem to be analyzed in this paper deals with the finding of n values x1, x2, ..., xn ∈ R which minimize the function:
E [míni=1,...,n c (ξ - xi)]
where ξ is a one-dimensional random variable with known distribution function φ and c is a measurable and positive function.
First, conditions on c in order to ensure the existence of a solution to this problem are determined. Next, necessary conditions to be satisfied by the point (x1, x2, ..., xn) in which the function attains the minimum are looked for. Finally, conditions on φ are given to guarantee the uniqueness of the point which verifies the necessary conditions for minimum, when the function c is c(y) = |y| and c(y) = y2.
@article{urn:eudml:doc:40648,
title = {Estimaci\'on bayesiana m\'ultiple de un par\'ametro.},
journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa},
volume = {32},
year = {1981},
pages = {95-115},
zbl = {0509.62030},
mrnumber = {MR0697197},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40648}
}
Vélez Ibarrola, Ricardo. Estimación bayesiana múltiple de un parámetro.. Trabajos de Estadística e Investigación Operativa, Tome 32 (1981) pp. 95-115. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40648/