On the trace approximations of products of Toeplitz matrices

TL;DR

This paper analyzes the accuracy of integral limit approximations for the traces of products of Toeplitz matrices, which are crucial in statistical analysis of stationary processes and spectral estimation.

Contribution

It establishes error orders and bounds for these approximations, advancing the theoretical understanding of Toeplitz matrix trace estimations.

Findings

Derived error bounds for trace approximations

Quantified approximation accuracy in statistical applications

Enhanced understanding of spectral parameter estimation

Abstract

The paper establishes error orders for integral limit approximations to the traces of products of Toeplitz matrices generated by integrable real symmetric functions defined on the unit circle. These approximations and the corresponding error bounds are of importance in the statistical analysis of discrete-time stationary processes: asymptotic distributions and large deviations of Toeplitz type random quadratic forms, estimation of the spectral parameters and functionals, etc.