Optimal estimation of sparse correlation matrices of semiparametric Gaussian copulas

Lingzhou Xue, Hui Zou

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Statistical inference of semiparametric Gaussian copulas is well studied in the classical fixed dimension and large sample size setting. Nevertheless, optimal estimation of the correlation matrix of semiparametric Gaussian copula is understudied, especially when the dimension can far exceed the sample size. In this paper we derive the minimax rate of convergence under the matrix l1-norm and l2-norm for estimating large correlation matrices of semiparametric Gaussian copulas when the correlation matrices are in a weak lq ball. We further show that an explicit rank-based thresholding estimator adaptively attains minimax optimal rate of convergence simultaneously for all 0 ≤ q < 1. Numerical examples are provided to demonstrate the finite sample performance of the rank-based thresholding estimator.

Original languageEnglish (US)
Pages (from-to)201-209
Number of pages9
JournalStatistics and its Interface
Volume7
Issue number2
DOIs
StatePublished - 2014

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Optimal Estimation
Correlation Matrix
Copula
Sparse matrix
Thresholding
Sample Size
Minimax Rate
Estimator
Optimal Rate of Convergence
L1-norm
Statistical Inference
Minimax
Exceed
Rate of Convergence
Ball
Norm
Numerical Examples
Demonstrate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

Cite this

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Optimal estimation of sparse correlation matrices of semiparametric Gaussian copulas. / Xue, Lingzhou; Zou, Hui.

In: Statistics and its Interface, Vol. 7, No. 2, 2014, p. 201-209.

Research output: Contribution to journalArticle

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