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

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 the almost sure convergence of a sequence of high-resolution spectral estimators indexed by the sample size.