Model-Free Estimation of Large Variance Matrices
AbstractThis 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.
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Bibliographic InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 17_10.
Date of creation: Jan 2010
Date of revision:
variance matrices; ill-conditioning; mean squared error; mean absolute deviations; resampling;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
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