Design-Free Estimation of Variance Matrices

43 Pages Posted: 9 Aug 2011 Last revised: 20 Nov 2014

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Walter Distaso

Imperial College Business School

Filip Zikes

Imperial College London

Date Written: November 20, 2011

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, especially when the data are generated from fat-tailed densities.

Keywords: Variance matrices, ill-conditioning, mean squared error, mean absolute deviations, resampling

Suggested Citation

Abadir, Karim M. and Distaso, Walter and Zikes, Filip, Design-Free Estimation of Variance Matrices (November 20, 2011). Available at SSRN: https://ssrn.com/abstract=1907266 or http://dx.doi.org/10.2139/ssrn.1907266

Karim M. Abadir

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Walter Distaso

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Filip Zikes (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

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