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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.

MSC:

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
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