Sample cumulants of stationary processes: asymptotic results

In this paper, we present the formulas of the covariances of the second-, third-, and fourth-order sample cumulants of stationary processes. These expressions are then used to obtain the analytic performance of FIR system identification methods as a function of the coefficients and the statistics of the input sequence. The lower bound in the variance is also compared for different sets of sample statistics to provide insight about the information carried by each sample statistic. Finally, the effect that the presence of noise has on the accuracy of the estimates is studied analytically. The results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal-to-noise ratio. Monte Carlo simulations are also included to compare their results with the predicted analytic performance