The Estimation of the Fourth-Order Cumulant for Dependent Data: Consistency and Asymptotic Normality

摘要

Let {Xi} be a stationary dependent random process with finite eight-order moments. For broad classes of processes (¿-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=1 n . We also establish the asymptotic distribution of the estimation error. The asymptotic expression of the variance is explicitly specified.