Second Errata Corrige to the Paper: “Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions”

In this second Errata Corrige, we would like to draw the reader’s attention to an error that we made in the derivation of the semiparametric Slepian-Bangs formula proposed in [1, Sect. IV]. Specifically, it is important to note that the expressions of the efficient semiparametric score vector $\bar{\mathbf{s}}_{\boldsymbol{\theta}_{0}}$ and the related semiparametric efficient FIM $\bar{\mathbf{I}}_{\boldsymbol{\theta}_{0}}$ derived in eqs. (43) and (46) of [1] are incorrect. In fact, in the derivation proposed in [1], the projection was incorrectly taken with respect to the “unconstrained” nuisance tangent space $\mathcal{T}_{g_{0}}^{u}$, whereas $\mathbf{s}_{\boldsymbol{\theta}_{0}}$ must be projected onto the “constrained” one, i.e. $\mathcal{T}_{\bar{g}_{0}}^{c}$.