A study on the empirical distribution of the scaled Hankel matrix eigenvalues

Hossein Hassani; Nader Alharbi; Mansi Ghodsi

doi:10.1016/j.jare.2014.08.008

A study on the empirical distribution of the scaled Hankel matrix eigenvalues

J Adv Res. 2015 Nov;6(6):925-9. doi: 10.1016/j.jare.2014.08.008. Epub 2014 Sep 2.

Authors

Hossein Hassani¹, Nader Alharbi², Mansi Ghodsi²

Affiliations

¹ The Statistical Research Centre, Bournemouth University, Bournemouth BH8 8EB, UK ; Institute for International Energy Studies (IIES), 65, Sayeh St., Vali-e-Asr Ave., Tehran 1967743 711, Iran.
² The Statistical Research Centre, Bournemouth University, Bournemouth BH8 8EB, UK.

Abstract

The empirical distribution of the eigenvalues of the matrix XX(T) divided by its trace is evaluated, where X is a random Hankel matrix. The distribution of eigenvalues for symmetric and nonsymmetric distributions is assessed with various criteria. This yields several important properties with broad application, particularly for noise reduction and filtering in signal processing and time series analysis.

Keywords: Eigenvalue; Hankel matrix; Noise reduction; Random process; Time series.