Efficient estimation in the semiparametric normal regression-copula model with a focus on QTL mapping. (English) Zbl 1327.62192

Basrak, Bojan; Klaassen, Chris A. J.

Banerjee, M. (ed.) et al., From probability to statistics and back: high-dimensional models and processes. A Festschrift in honor of Jon A. Wellner. Including papers from the conference, Seattle, WA, USA, July 28–31, 2010. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-83-6). Institute of Mathematical Statistics Collections 9, 20-32 (2013).

Summary: The semiparametric normal copula model is studied with a correlation matrix that depends on a covariate. The bivariate version of this regression-copula model has been proposed for statistical analysis of Quantitative Trait Loci (QTL) via twin data. Appropriate linear combinations of Van der Waerden’s normal scores rank correlation coefficients yield \(\sqrt{n}\)-consistent estimators of the coefficients in the correlation function, i.e. of the regression parameters. They are used to construct semiparametrically efficient estimators of the regression parameters.
For the entire collection see [Zbl 1319.62002].

MSC:

62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

semiparametric inference; Van der Waerden; \(\sqrt{n}\)-consistency; linkage analysis; QTL mapping