In this paper we introduce $E$-ancillarity and complete $E$-sufficiency, natural extensions of the definitions of ancillarity and complete sufficiency to a space of estimating or inference functions. These are functions of both the data and the parameter. We begin either with a space of all such functions or with a subset defined to exploit special features of a model; for example, we allow restrictions to inference functions that are linear in the observations or linear in the parameter. Subsequently, a reduction analogous to complete sufficiency is carried out, and within the complete $E$-sufficient space of inference functions, one is chosen with properties that we deem desirable.
Publié le : 1988-06-14
Classification:
Estimating function,
score function,
sufficiency,
local sufficiency,
ancillarity,
completeness,
nuisance parameter,
Rao-Blackwell theorem,
62A99,
62B99
@article{1176350819,
author = {Small, Christopher G. and McLeish, D. L.},
title = {Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 534-551},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350819}
}
Small, Christopher G.; McLeish, D. L. Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space. Ann. Statist., Tome 16 (1988) no. 1, pp. 534-551. http://gdmltest.u-ga.fr/item/1176350819/