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.
@article{1176348268,
author = {Chang, I.-Shou and Hsiung, Chao A.},
title = {An $E$-Ancillarity Projection Property of Cox's Partial Score Function},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 1651-1660},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348268}
}
Chang, I.-Shou; Hsiung, Chao A. An $E$-Ancillarity Projection Property of Cox's Partial Score Function. Ann. Statist., Tome 19 (1991) no. 1, pp. 1651-1660. http://gdmltest.u-ga.fr/item/1176348268/