Estimating the real parameter in a two-sample proportional odds model. (English) Zbl 0829.62031

Summary: 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.


62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
45H05 Integral equations with miscellaneous special kernels
62F10 Point estimation
Full Text: DOI