The Annals of Statistics

Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space

Christopher G. Small and D. L. McLeish

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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.

Article information

Source
Ann. Statist., Volume 16, Number 2 (1988), 534-551.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350819

Digital Object Identifier
doi:10.1214/aos/1176350819

Mathematical Reviews number (MathSciNet)
MR947561

Zentralblatt MATH identifier
0684.62012

JSTOR
links.jstor.org

Subjects
Primary: 62A99: None of the above, but in this section
Secondary: 62B99: None of the above, but in this section

Keywords
Estimating function score function sufficiency local sufficiency ancillarity completeness nuisance parameter Rao-Blackwell theorem

Citation

Small, Christopher G.; McLeish, D. L. Generalizations of Ancillarity, Completeness and Sufficiency in an Inference Function Space. Ann. Statist. 16 (1988), no. 2, 534--551. doi:10.1214/aos/1176350819. https://projecteuclid.org/euclid.aos/1176350819


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