Estimating the Real Parameter in a Two-Sample Proportional Odds Model

This paper considers efficient estimation of the Euclidean parameter in the proportional odds model G (1 - G) ^-1 = F (1 - F) ^-1 when two independent i. i. d. samples with distributions F and G, respectively, are observed. The Fisher information I () 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 N-consistent estimate and shown to be asymptotically efficient in the sense that its asymptotic risk achieves the corresponding minimax lower bound.