This paper considers efficient estimation of the Euclidean parameter $\theta$ in the proportional odds model $G(1 - G)^{-1} = \theta F(1 - F)^{-1}$ when two independent i.i.d. samples with distributions $F$ and $G$, respectively, are observed. The Fisher information $I(\theta)$ is calculated based on the solution of a pair of integral equations which are derived from a class of more general semiparametric models. A one-step estimate is constructed using an initial $\sqrt N$-consistent estimate and shown to be asymptotically efficient in the sense that its asymptotic risk achieves the corresponding minimax lower bound.
@article{1176324526,
author = {Wu, Colin O.},
title = {Estimating the Real Parameter in a Two-Sample Proportional Odds Model},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 376-395},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324526}
}
Wu, Colin O. Estimating the Real Parameter in a Two-Sample Proportional Odds Model. Ann. Statist., Tome 23 (1995) no. 6, pp. 376-395. http://gdmltest.u-ga.fr/item/1176324526/