This paper presents a new approach to characterize nanoparticles using derivatives of scattering profiles of evanescent waves/surface plasmons. We start the procedure using the scattering profiles for an unknown configuration of nanoparticles, either from physical experiments or numerical simulations conducted for different nanoparticles on surfaces. We apply the statistical technique of compound estimation to recover the derivatives of scattering profiles. The L(1) discrepancies with the corresponding curves from known configurations are used to identify the most plausible configuration of particles that could yield the "experimental" profiles. We conduct a simulation study to see how often the new procedure correctly recovers the agglomeration level for gold spherical nanoparticles on a thin gold film. The results suggest that first derivatives are much more effective for characterization than undifferentiated profiles and that M(33) is the most useful element for distinguishing among configurations. The proposed compound estimation technique is more effective than typical inverse analyses based on look-up tables and can be used effectively in nanoparticle characterization platforms.