Rank-based Tapering Estimation of Bandable Correlation Matrices

The nonparanormal model assumes that variables follow a multivariate normal distribution after a set of unknown monotone increasing transformations. It is a flexible generalization of the normal model but retains the nice interpretability of the latter. In this paper we propose a rank-based tapering estimator for estimating the correlation matrix in the nonparanormal model in which the variables have a natural order. The rank-based tapering estimator does not require knowing or estimating the monotone transformation functions. We establish the rates of convergence of the rank-based tapering under Frobenius and matrix operator norms, where the dimension is allowed to grow at a nearly exponential rate relative to the sample size. Monte Carlo simulation is used to demonstrate the finite performance of the rank-based tapering estimator. A data example is used to illustrate the nonparanormal model and the efficacy of the proposed rank-based tapering estimator.