Almost all contemporary statistical modeling techniques are designed for real-valued data. However, complex-valued random vectors are frequently encountered in several important big data applications. For instance, in functional magnetic resonance imaging (fMRI), the raw data produced by scanners consist of complex numbers. Similarly, in nuclear power plants, the periodic inspection of steam generator tubes involves complex measurements obtained through Eddy-current probes. Developing a comprehensive theory of statistical inference for complex-valued random vectors is therefore essential.
