Special Lecture

The normal scores estimator for the high-dimensional Gaussian copula model
Tuesday, 12 February 2019 - 2:30 pm to 4:00 pm
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TITLE: The normal scores estimator for the high-dimensional Gaussian copula model SPEAKER: Yue Zhao (KU Leuven) DATE: Tuesday, February 12, 2019 TIME: 2:30 pm ROOM: STM664 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 an Euclidean parameter $R$ called the copula correlation matrix. In this talk we study the normal scores (rank correlation coefficient) estimator, also known as the van der Waerden coefficient, 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.