I have a nonlinear regression problem, and the noise is assumed iid gaussian. The nonlinear function is complex-valued.
From the book "Linear and Graphical Models for the multivariate complex normal distribution", Anderson et. al, Lecture notes in Statistics #101 page 26, a p-dimensional complex normal distribution can be written as a 2p-dimensional real normal distribution.
Then why study complex normal separately ? Does at any place in statistics or probability, complex-valuedness makes a difference (for normal distribution per se) ?