Almost all current statistical modelling techniques are designed for real-valued data. Though, complex-valued random vectors are common in some important applications of big data. For instance, in functional magnetic resonance imaging (fMRI), the raw data returned by the scanner are complex numbers. For steam generator tubes in nuclear power plants, defects are periodically checked by means of complex Eddy-current probes measurements. It is thus important to build a complete theory of statistical inference for complex-valued random vectors.