The estimation of the fourth-order cumulant for dependent data: consistency and asymptotic normality

Authors:
Elias Masry
Affiliations:
Department of Electrical and Computer Engineering, University of California, San Diego
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

Let{Xi} be a stationary dependent random process with finite eight-order moments. For broad classes of processes (ρ -mixing and strongly mixing), we obtain the convergence in probability, with sharp rates, of the estimate of the fourth-order cumulant from n observations {Xi}i=1n. We also establish the asymptotic distribution of the estimation error. The asymptotic expression of the variance is explicitly specified.