Sample distributions of the partial correlation coefficients of a complex autoregressive process

The asymptotic distributions of the sample estimates of the partial correlation coefficients (PCORs) of a complex Gaussian AR (autoregressive) process are derived. Unlike the PDF (probability density function) of the sample model coefficients, which is asymptotically complex Gaussian distributed and has a form similar to that for a real AR process, the PDF of sample PCORs cannot be simply expressed in a complex Gaussian form. Rather, the real and imaginary parts of sample PCORs have a jointly real Gaussian distribution, whose covariance matrix can be evaluated through a recursive algorithm. Computer simulations have been performed confirming the correctness of the theory. Although the PDFs are derived on the basis of a large-sample theory, computer results show that they work quite well even for small samples; this is important to some applications such as radar