Semiparametric Slepian-Bangs Formula for Complex Elliptically Symmetric Distributions

TL;DR

This paper derives a semiparametric Slepian-Bangs formula for complex elliptically symmetric distributions, enabling the calculation of lower bounds on estimator performance in the presence of unknown nuisance parameters.

Contribution

It introduces a novel semiparametric Slepian-Bangs formula for CES distributions, extending the classical bounds to more robust, real-world scenarios with unknown density generators.

Findings

Provides a new formula for CES distributions

Establishes a semiparametric Cramér-Rao bound

Enables robust parameter estimation analysis

Abstract

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 \textit{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.