Design-free estimation of variance matrices
File(s)
Accepted version
Author(s)
Abadir, KM
Distaso, W
Žikeš, F
Type
Journal Article
Abstract
This paper introduces a new method for estimating 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 deliver a well-conditioned estimator (by construction), even when there are fewer observations than dimensions. We also show that our estimator has lower error norms than the traditional one. Our estimator is design-free: we make no assumptions on the distribution of the random sample or on any parametric structure the variance matrix may have. Simulations confirm our theoretical results and they also show that our simple estimator does very well in comparison with other existing methods.
Date Issued
2014-08
Date Acceptance
2014-03-27
Citation
Journal of Econometrics, 2014, 181 (2), pp.165-180
ISSN
1872-6895
Publisher
Elsevier
Start Page
165
End Page
180
Journal / Book Title
Journal of Econometrics
Volume
181
Issue
2
Copyright Statement
© 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Variance matrices
Ill-conditioning
Mean squared error
Mean absolute deviations
Resampling
U-statistics
Publication Status
Published
Date Publish Online
2014-04-15