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Model-Free Estimation of Large Variance Matrices

Author

Listed:
  • Karim M. Abadir

    (Imperial College London)

  • Walter Distaso

    (Imperial College London)

  • Filip Žikeš

    (Imperial College London)

Abstract

This paper introduces a new method for estimating large variance matrices. Starting from the orthogonal decomposition of the sample variance matrix, we exploit the fact that orthogonal matrices are never ill-conditioned and therefore focus on improving the estimation of the eigenvalues. We estimate the eigenvectors from just a fraction of the data, then use them to transform the data into approximately orthogonal series that we use to estimate a well-conditioned matrix of eigenvalues. Our estimator is model-free: we make no assumptions on the distribution of the random sample or on any parametric structure the variance matrix may have. By design, it delivers well-conditioned estimates regardless of the dimension of problem and the number of observations available. Simulation evidence show that the new estimator outperforms the usual sample variance matrix, not only by achieving a substantial improvement in the condition number (as expected), but also by much lower error norms that measure its deviation from the true variance.

Suggested Citation

  • Karim M. Abadir & Walter Distaso & Filip Žikeš, 2010. "Model-Free Estimation of Large Variance Matrices," Working Paper series 17_10, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:17_10
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    More about this item

    Keywords

    variance matrices; ill-conditioning; mean squared error; mean absolute deviations; resampling;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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