Abstract
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.
Citation
Colin O. Wu. "Estimating the Real Parameter in a Two-Sample Proportional Odds Model." Ann. Statist. 23 (2) 376 - 395, April, 1995. https://doi.org/10.1214/aos/1176324526
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