Stein ' s Phenomenon and Nanoparticle Characterization

Motivated by the possibility of engineering nanostructured surfaces for efficient nano-thermophotovoltaic power generation, we investigate whether and how Stein's phenomenon may effectively be incorporated into nanoparticle characterization based on scattering data. The statistical innovation in our approach is to employ a form of nonlinear shrinkage in the compound estimation of scattering profiles and their derivatives, such that the estimation error is reduced without destroying the self-consistency property of compound estimation (i.e., that the estimated derivatives are precisely the derivatives of the estimated scattering profiles). Our numerical experiments found that the estimation error may be reduced by up to 7%, 25%, and 31% respectively in estimating the scattering profiles, their first derivatives, and their second derivatives. Surprisingly, the reduced estimation error does not translate into demonstrably superior correct classification rates for nanoparticle configurations. Speculations on the findings and promising avenues for future research are discussed.