AN E-ANCILLARITY PROJECTION PROPERTY OF COXS PARTIAL SCORE FUNCTION

This paper shows that Cox's partial score function is the projection of the score function on the (locally) E-ancillary subspace for the nuisance parameter (Small and McLeish). This is done by adapting the concepts of (locally) E-ancillarity and (locally) E-sufficiency for inference functions (McLeish and Small) to an extended Cox's regression model, where the baseline function is allowed to be a predictable process.