Efficient Estimation in the Bivariate Normal Copula Model: Normal Margins Are Least Favourable

Efficient estimation in the semiparametric normal regression-copula model with a focus on QTL mapping

“…The Van der Waerden normal scores rank correlation coefficient is such an adaptive estimator of in the presence of σ, as has been shown by Klaassen and Wellner [9].…”

“…This classic semiparametric normal copula model has been studied in Klaassen and Wellner [9]. They show that at ( 0 , ψ 0 (·)) with | 0 | < 1 the least favorable parametric submodel of the semiparametric model from (2.1) for estimating the correlation coefficient is the correlation-scale model that we get by restricting the nonparametric class of transformations ψ(·) to the one-dimensional parametric class of transformations…”

“…The paper Klaassen and Wellner [9] is fundamental to the present paper, is based on Jon's ideas, and was written on his initiative. Bojan Basrak gratefully acknowledges friendship and hospitality of Eurandom staff and colleagues during his postdoctoral studies at the institute.…”

“…In the normal regression-copula model of (1.2) the Van der Waerden normal scores rank correlation coefficientρ n (z) that is based on all observations with Z i = z, is semiparametrically efficient in estimating + γz, z = −1, 0, 1, as follows from Klaassen and Wellner [9]. One would guess then that…”

Chapter 10 Finite samples and asymptotics

“…In any case, these papers are still being cited because of their relevance to the study of semiparametric copula models. For example the Van der Waerden normal scores rank correlation coefficient is semiparametrically efficient in the normal copula model; see Klaassen and Wellner (1997). In the normal copula model one assumes that if all components of a random vector are transformed into normal random variables, then the resulting random vector has a multivariate normal distribution.…”