A Complete Class Theorem for Statistical Problems with Finite Sample Spaces

Brown, Lawrence D.

Ann. Statist., Tome 9 (1981) no. 1, p. 1289-1300 / Harvested from Project Euclid

Résumé

This paper contains a complete class theorem (Theorem 3.2) which applies to most statistical estimation problems having a finite sample space. This theorem also applies to many other statistical problems with finite sample spaces. The description of this complete class involves a stepwise algorithm. At each step of the process it is necessary to construct the Bayes procedures in a suitably modified version of the original problem. The complete class is a minimal complete class if the loss function is strictly convex. Some examples are given to illustrate the application of this complete class theorem. Among these is a new result concerning the estimation of the parameters of a multinomial distribution under a normalized quadratic loss function. (See Example 4.5).

Publié le : 1981-11-14
Classification: Complete class theorem, finite sample space, admissible procedures, Bayes procedure, estimation, binomial distribution, multinomial distribution, strictly convex loss, squared error loss, maximum likelihood estimate, 62C07, 62C15, 62F10, 62F11, 62C10

@article{1176345645,
     author = {Brown, Lawrence D.},
     title = {A Complete Class Theorem for Statistical Problems with Finite Sample Spaces},
     journal = {Ann. Statist.},
     volume = {9},
     number = {1},
     year = {1981},
     pages = { 1289-1300},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345645}
}

Brown, Lawrence D. A Complete Class Theorem for Statistical Problems with Finite Sample Spaces. Ann. Statist., Tome 9 (1981) no. 1, pp.  1289-1300. http://gdmltest.u-ga.fr/item/1176345645/