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February 1997 Efficient estimation in the bivariate normal copula model: normal margins are least favourable
Chris A.J. Klaassen, Jon A. Wellner
Bernoulli 3(1): 55-77 (February 1997).


Consider semi-parametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter θ of interest and in which the two unknown marginal distributios are the (infinite-dimensional) nuisance parameters. The efficient score for θ can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. Where the family of copula functions corresponds to the normal distributios with mean 0, variance 1 and correlation θ, the solution of these equations is given, and we thereby show that the normal scores rank correlation coefficient is asymptotically efficient. We also show that the bivariate normal model with equal variances constitutes the least favourable parametric submodel. Finally, we discuss the interpretation of |θ| in the normal copula model as the maximum (monotone) correlation coefficient.


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Chris A.J. Klaassen. Jon A. Wellner. "Efficient estimation in the bivariate normal copula model: normal margins are least favourable." Bernoulli 3 (1) 55 - 77, February 1997.


Published: February 1997
First available in Project Euclid: 4 May 2007

zbMATH: 0877.62055
MathSciNet: MR1466545

Keywords: bivariate normal , Copula models , Correlation , coupled differential equations , Information , maximum correlation , normal scores , projection equations , rank correlation , semi-parametric model , Sturm-Liouville equations

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 1 • February 1997
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