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On the sparsity of signals in a random sample

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  • Binyan Jiang
  • Wei-Liem Loh

Abstract

This article proposes a method of moments technique for estimating the sparsity of signals in a random sample. This involves estimating the largest eigenvalue of a large Hermitian trigonometric matrix under mild conditions. As illustration, the method is applied to two well-known problems. The first focuses on the sparsity of a large covariance matrix and the second investigates the sparsity of a sequence of signals observed with stationary, weakly dependent noise. Simulation shows that the proposed estimators can have significantly smaller mean absolute errors than their main competitors. Copyright 2012, Oxford University Press.

Suggested Citation

  • Binyan Jiang & Wei-Liem Loh, 2012. "On the sparsity of signals in a random sample," Biometrika, Biometrika Trust, vol. 99(4), pages 915-928.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:4:p:915-928
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    File URL: http://hdl.handle.net/10.1093/biomet/ass039
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    Cited by:

    1. Binyan Jiang, 2015. "An empirical estimator for the sparsity of a large covariance matrix under multivariate normal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 211-227, April.
    2. Jiang, Binyan, 2013. "Covariance selection by thresholding the sample correlation matrix," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2492-2498.

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