Title: The normal scores estimator for the high-dimensional Gaussian copula model
Authors: Yue Zhao - KU Leuven (Belgium) [presenting]
Christian Genest - McGill University (Canada)
Abstract: The (semiparametric) Gaussian copula model consists of distributions that have dependence structure described by Gaussian copulas but that have arbitrary marginals. A Gaussian copula is in turn determined by a Euclidean parameter R called the copula correlation matrix. We study the normal scores (rank correlation) estimator, also known as the van der Waerden estimator, of R in high dimensions. It is well known that in fixed dimensions, the normal scores estimator is the optimal estimator of R, i.e., it has the smallest asymptotic covariance. Curiously though, in high dimensions, nowadays the preferred estimators of R are usually based on Kendall's tau or Spearman's rho. We show that the normal scores estimator in fact remains the optimal estimator of R in high dimensions. More specifically, we show that the approximate linearity of the normal scores estimator in the efficient influence function, which in fixed dimensions implies the optimality of this estimator, holds in high dimensions as well.