A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. (English) Zbl 0831.62030

Genest, C.; Ghoudi, K.; Rivest, L.-P.

Biometrika 82, No. 3, 543-552 (1995).

Summary: This paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions. The proposed estimator, obtained as a solution of a pseudo-likelihood equation, is shown to be consistent, asymptotically normal and fully efficient at independence. A natural estimator of its asymptotic variance is proved to be consistent. Comparisons are made with alternative semiparametric estimators in the special case of D. G. Clayton’s [ibid. 65, 141-151 (1978; Zbl 0394.92021)]model for association in bivariate data.

MSC:

62G05	Nonparametric estimation
62H12	Estimation in multivariate analysis
62E20	Asymptotic distribution theory in statistics
62G20	Asymptotic properties of nonparametric inference

Keywords:

Clayton’s bivariate family; Kendall’s tau; multivariate rank statistic; pseudo-likelihood; consistency; asymptotic normality; efficiency; pseudo- likelihood equation; asymptotic variance; semiparametric estimators

Citations:

Zbl 0394.92021