Characterization of statistical models for which a given statistic has the same distribution.

Han-Ping Li (1)

1 IRMA - Institut de Recherche Mathématique Avancée

In this paper, a rather general method to characterize the statistical models for which a given statistic has the same distribution is given. First, the semi-parametric transformation model and non-parametric transformation model are characterized in term of random transformations, with the independence in the first model, without the independence in the second one. By applying these characterizations, the problem of describing all all distributions for which the distribution of $T$ is the same can be solved by first finding a suitable group of transformations for which $T$ is a maximal invariant and then applying a random transformation on a suitable random variable. Many statistical applications are given, including the characterization of the statistical models for which a Fisher's or Student's statistic has the same distribution.

Mots clés: group Model; random transformation; "group Model; transformation Model; distributions characterization; random transformation"

Domaines: Statistiques [math.ST]

Han-Ping Li. Characterization of statistical models for which a given statistic has the same distribution.. 2000. ⟨hal-00129659⟩