Semiparametric Slepian-Bangs Formula for Complex Elliptically Symmetric Distributions

This letter aims at deriving a Semiparametric Slepian-Bangs (SSB) formula for Complex Elliptically Symmetric (CES) distributed data vectors. The Semiparametric Cram'{e}r-Rao Bound (SCRB), related to the proposed SSB formula, provides a lower bound on the Mean Square Error (MSE) of $\mathit{\text{any}}$ robust estimator of a parameter vector parameterizing the mean vector and the scatter matrix of the given CES-distributed vector in the presence of an unknown, nuisance, density generator.