A theorem is proved showing that, assuming some boundary conditions, the following hypotheses:
1. {Xn} is a sequence of continuous random variables which approaches in probability to a numerical sequence {an},
2. {Yn} is another sequence of random variables such that, for all n, the density function of Yn is proportional to the product of the density of Xn by another density not depending on n,
lead to the fact that the random sequence {Yn} also approaches in probability to {an}.
We also show some related theorems as well as its application to the Bayesian inference.
@article{urn:eudml:doc:40414,
title = {Un teorema de convergencia con aplicaci\'on a la inferencia bayesiana.},
journal = {Trabajos de Estad\'\i stica},
volume = {1},
year = {1986},
pages = {30-41},
zbl = {0654.62031},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40414}
}
Gómez Sánchez-Manzano, Eusebio. Un teorema de convergencia con aplicación a la inferencia bayesiana.. Trabajos de Estadística, Tome 1 (1986) pp. 30-41. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40414/