This paper shows the statistics that define the likelihood ratio tests about the mean of a k-dimensional normal population, when the hypotheses to test are H0: θ = 0; H0*: θ ∈ τφ; H1: θ ∈ τ; H2: θ ∈ Rk, being τ a closed and poliedric convex cone in Rk, and τφ the minima dimension face in τ.
It is proved that the obtained statistics distributions are certain combinations of chi-squared distributions, when θ = 0.
At last, it is proved that the power functions of the tests satisfy some desirable properties.
@article{urn:eudml:doc:40781,
title = {Tests de la raz\'on de verosimilitud para medias de poblaciones normales, sujetas a restricciones.},
journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa},
volume = {35},
year = {1984},
pages = {305-318},
zbl = {0731.62109},
mrnumber = {MR0829691},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40781}
}
Menéndez Fernández, José Antonio. Tests de la razón de verosimilitud para medias de poblaciones normales, sujetas a restricciones.. Trabajos de Estadística e Investigación Operativa, Tome 35 (1984) pp. 305-318. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40781/