Unbiased Efficient Estimator of the Fourth-Order Cumulant for Random Zero-Mean Non-i.i.d. Signals: Particular Case of MA Stochastic Process

Non-Gaussian processes may require not only the information provided by first two moments, but also that given by the higher-order statistics, in particular, by the third- and fourth-order moments or cumulants. This paper addresses a fourth-order cumulant estimation problem for real discrete-time random non-i.i.d. signal, that can be approximated as an MA stochastic process. An unbiased estimator is proposed, studied and compared to two other frequently used estimators of the fourth-order cumulant (natural estimator and fourth
$k$
-statistics). Statistical comparative studies are undertaken from both bias and MSE points of view, for different distribution laws and MA filters. Algorithms, aiming to reduce computational complexity of the proposed estimator, as well as that of the fourth
$k$
-statistics bias, are also provided.