Mathematical tools based on cross correlations between aerodynamic quantities of interest inside the shear flow region and the radiated sound pressure are used to investigate noise generation mechanisms in a plane compressible mixing layer. An original methodology relying on an efficient coupling between proper orthogonal decomposition (POD) and stochastic estimation procedures is developed to analyze the main aerodynamic mechanisms that govern noise production. POD is used to split the instantaneous flow fluctuations as the sum of three components: the large-and small-scale coherent structures (LCS and SCS) and the background quasi-Gaussian fluctuations. Based on this flow partitioning, quadratic stochastic estimation is implemented to estimate the far-field acoustic pressure associated with each flow component. The far field acoustic pressure associated with both LCS and SCS is then investigated. By analyzing the RMS and temporal spectra of the far-field acoustic pressure, it is observed that the SCSs, as defined thanks to the POD basis, are responsible for the main part of the noise emission.