Open Access
June, 1988 Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space
Christopher G. Small, D. L. McLeish
Ann. Statist. 16(2): 534-551 (June, 1988). DOI: 10.1214/aos/1176350819

Abstract

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.

Citation

Download Citation

Christopher G. Small. D. L. McLeish. "Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space." Ann. Statist. 16 (2) 534 - 551, June, 1988. https://doi.org/10.1214/aos/1176350819

Information

Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0684.62012
MathSciNet: MR947561
Digital Object Identifier: 10.1214/aos/1176350819

Subjects:
Primary: 62A99
Secondary: 62B99

Keywords: ancillarity , completeness , estimating function , local sufficiency , nuisance parameter , Rao-Blackwell theorem , score function , sufficiency

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • June, 1988
Back to Top