Bernoulli

  • Bernoulli
  • Volume 24, Number 4B (2018), 3833-3863.

Covariance estimation via sparse Kronecker structures

Chenlei Leng and Guangming Pan

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Abstract

The problem of estimating covariance matrices is central to statistical analysis and is extensively addressed when data are vectors. This paper studies a novel Kronecker-structured approach for estimating such matrices when data are matrices and arrays. Focusing on matrix-variate data, we present simple approaches to estimate the row and the column correlation matrices, formulated separately via convex optimization. We also discuss simple thresholding estimators motivated by the recent development in the literature. Non-asymptotic results show that the proposed method greatly outperforms methods that ignore the matrix structure of the data. In particular, our framework allows the dimensionality of data to be arbitrary order even for fixed sample size, and works for flexible distributions beyond normality. Simulations and data analysis further confirm the competitiveness of the method. An extension to general array-data is also outlined.

Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3833-3863.

Dates
Received: June 2016
Revised: April 2017
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1524038771

Digital Object Identifier
doi:10.3150/17-BEJ980

Mathematical Reviews number (MathSciNet)
MR3788190

Zentralblatt MATH identifier
06869893

Keywords
covariance matrix Kronecker structure matrix data non-asymptotic bound

Citation

Leng, Chenlei; Pan, Guangming. Covariance estimation via sparse Kronecker structures. Bernoulli 24 (2018), no. 4B, 3833--3863. doi:10.3150/17-BEJ980. https://projecteuclid.org/euclid.bj/1524038771


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