Limiting Behavior of Functionals of Higher-Order Sample Cumulant Spectra

Abstract

This paper is concerned with establishing a broad class of estimators (and the limiting behavior, thereof) for parametrizations of higher than second-order structure. This includes parametrizations which reflect, for example, such properties as nonlinearity and/or non-Gaussianity and/or time irreversibility. Asymptotic distributions, almost-sure convergence, and probability-one bounds for such estimators are established. Several applications of such estimators are discussed.