On the Statistical Consistency of a Generalized Cepstral Estimator

TL;DR

This paper addresses the challenge of estimating generalized cepstral coefficients for stationary processes, proposing a consistent estimator that improves upon naive methods and enables reliable system identification.

Contribution

It introduces a novel consistent estimator for generalized cepstral coefficients and demonstrates its application to cascade linear stochastic systems.

Findings

Naive periodogram-based estimator is inconsistent.

Proposed estimator achieves statistical consistency.

Application to cascade systems yields reliable system identification.

Abstract

We consider the problem to estimate the generalized cepstral coefficients of a stationary stochastic process or stationary multidimensional random field. It turns out that a naive version of the periodogram-based estimator for the generalized cepstral coefficients is not consistent. We propose a consistent estimator for those coefficients. Moreover, we show that the latter can be used in order to build a consistent estimator for a particular class of cascade linear stochastic systems.