Matrix spectral norm Wielandt inequalities with statistical applications

Jibo Wu,Wende Yi

doi:10.1186/1029-242x-2014-110

Abstract

In this article, we construct a new matrix spectral norm Wielandt inequality. Then we apply it to give the upper bound of a new measure of association. Finally, a new alterative based on the spectral norm for the relative gain of the covariance adjusted estimator of parameters vector is given.

Highlights

Wang and Ip [ ] have extended the Wielandt inequality to the matrix version, which can be expressed as follows
Suppose that A is an n × n positive definite symmetric matrix, x and y are two nonnull real vectors satisfying x y = such that x (x Ay) Ax · y Ay ≤λ – λn λ + λn ( )where λ ≥ · · · ≥ λn > are the ordered eigenvalues of A
In Section, we present a matrix spectral norm versions of the Wielandt inequality

Summary

Introduction

Wang and Ip [ ] have extended the Wielandt inequality to the matrix version, which can be expressed as follows. Drury et al [ ] introduced the matrix, determinant and trace version of the Wielandt inequality. Liu et al [ ] has improved two matrix trace Wielandt inequalities and proposed their statistical applications. Wang and Yang [ ] presented the Euclidean norm matrix Wielandt inequality and showed the statistical applications.

Results

Conclusion