Methods and Performances Study for Power Spectrum Density Modeling of Non-gaussian Processes

As used in Gaussian case, the autoregressive model can be applied to fit the power spectrum density of non-Gaussian processes. However, the least square estimation, the most popular method under Gaussian hypothesis, is no more efficient here. Firstly, under the non-Gaussian hypothesis of Gaussian mixture, the Crammer-Rao bounds of parameter estimation for the power spectrum density autoregressive model are analyzed. Secondly, the efficient estimation, i.e. the maximum likelihood estimation, is deduced. Thirdly, its simplification, the weighted least square estimation is set up. Finally, a numerical instance is given to illustrate the performance discrimination among the maximum likelihood estimation, the weighted least square estimation and the conventional unweighted least square estimation.