Bernoulli

Efficient estimation in the bivariate normal copula model: normal margins are least favourable

Chris A.J. Klaassen and Jon A. Wellner

Full-text: Open access

Abstract

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.

Article information

Source
Bernoulli, Volume 3, Number 1 (1997), 55-77.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1178291932

Mathematical Reviews number (MathSciNet)
MR1466545

Zentralblatt MATH identifier
0877.62055

Keywords
bivariate normal copula models correlation coupled differential equations information maximum correlation normal scores projection equations rank correlation semi-parametric model Sturm-Liouville equations

Citation

Klaassen, Chris A.J.; Wellner, Jon A. Efficient estimation in the bivariate normal copula model: normal margins are least favourable. Bernoulli 3 (1997), no. 1, 55--77. https://projecteuclid.org/euclid.bj/1178291932


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