Statistical analysis of speech is an emerging area of machine learning. In this paper, we tackle the biometric challenge of Automatic Speaker Verification (ASV) of differentiating between samples generated by two distinct populations of utterances, those of an authentic human voice and those generated by a synthetic one. Solving such an issue through a statistical perspective foresees the definition of a decision rule function and a learning procedure to identify the optimal classifier. Classical state-ofthe-art countermeasures rely on strong assumptions such as stationarity or local-stationarity of speech that may be atypical to encounter in practice. We explore in this regard a robust non-linear and nonstationary signal decomposition method known as the Empirical Mode Decomposition combined with the Mel-Frequency Cepstral Coefficients in a novel fashion with a refined classifier technique known as multi-kernel Support Vector machine. We undertake significant real data case studies covering multiple ASV systems using different datasets, including the ASVSpoof 2019 challenge database. The obtained results overwhelmingly demonstrate the significance of our feature extraction and classifier approach versus existing conventional methods in reducing the threat of cyber-attack perpetrated by synthetic voice replication seeking unauthorised access.