On variance of sample matrix eigenvalue

Abstract

The variance of a matrix eigenvalue estimator is considered. This estimator is a function of simple random sample variances and covariances of a multidimensional random variable whose distribution is not necessarily normal. The variance of the eigenvalue estimator is approximated based on the Taylor expansion for a function of simple random sample moments. A method for approximating the variance of the canonical correlation estimator is also proposed. A simulation analysis of the accuracy of variance estimation is presented. The considered approximation of variance can be applied to assessing the variance of a statistic which is the solution of any implicit interdependence functions of sample moments.

Keywords:

• Matrix eigenvalue
• Variance-covariance matrix
• Canonical correlation
• Approximation of variance

Additional information

Funding

This paper is a result of a grant supported by the National Science Center, Poland, no. 2016/21/B/HS4/00666