Parametric estimation of cumulants

The problem of higher-order cumulants estimation is addressed in this paper. Higher-order cumulants are necessary in many applications, such as blind source separation (BSS) and blind deconvolution. In these applications, the cumulants are usually estimated using sample estimation. In this paper, a parametric method for cumulants estimation using the Gaussian mixture model (GMM) is derived. The cumulants are expressed in terms of the GMM parameters, and estimated using the maximum-likelihood estimator. The performance of the proposed model-based method was evaluated and compared to sample estimation using computer simulations. The results show that the model-based estimation outperforms the sample estimation in terms of root-mean-square error.