Rank-based tapering estimation of bandable correlation matrices

Lingzhou Xue, Hui Zou

Research output: Contribution to journalArticle

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Abstract

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 interpretabil-ity 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.

Original languageEnglish (US)
Pages (from-to)83-100
Number of pages18
JournalStatistica Sinica
Volume24
Issue number1
DOIs
StatePublished - Jan 1 2014

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Keywords

  • Banding
  • Correlation matrix
  • Gaussian copula
  • Nonparanormal model
  • Tapering
  • Variable transformation

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