Generalizations of ancillarity, completeness and sufficiency in an inference function space. (English) Zbl 0684.62012

Small, Christopher G.; McLeish, D. L.

Ann. Stat. 16, No. 2, 534-551 (1988).

Summary: 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.

MSC:

62A01	Foundations and philosophical topics in statistics
62B99	Sufficiency and information
62B05	Sufficient statistics and fields

Keywords:

estimating function; score function; sufficiency; local sufficiency; completeness; nuisance parameter; Rao-Blackwell theorem; E-ancillarity; complete E-sufficiency; inference functions; complete sufficiency