On the well-posedness of multivariate spectrum approximation and convergence of high-resolution spectral estimators

TL;DR

This paper proves the well-posedness of multivariate spectrum approximation problems and demonstrates the almost sure convergence of high-resolution spectral estimators as sample size increases.

Contribution

It establishes the well-posedness of generalized moment problems and applies these results to prove convergence of spectral estimators.

Findings

Proved well-posedness of multivariate spectrum approximation problems.

Established almost sure convergence of high-resolution spectral estimators.

Extended previous work on spectral estimation methods.

Abstract

In this paper, we establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size.