TY - JOUR
T1 - Slepian-Bangs-type formulas and the related Misspecified Cramér-Rao Bounds for Complex Elliptically Symmetric distributions
AU - Mennad, Abdelmalek
AU - Fortunati, Stefano
AU - El Korso, Mohammed Nabil
AU - Younsi, Arezki
AU - Zoubir, Abdelhak M.
AU - Renaux, Alexandre
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - In this paper, Slepian-Bangs-type formulas for Complex Elliptically Symmetric distributed (CES) data vectors in the presence of model misspecification are provided. The basic Slepian-Bangs (SB) formula has been introduced in the array processing literature as a convenient and compact representation of the Fisher Information Matrix (FIM) for parameter estimation under (parametric) Gaussian data model. Extending recent results on this topic, in this paper, we provide a new generalization of the classical SB formula to parametric estimation problems involving non-Gaussian, heavy-tailed, CES distributed data in the presence of model misspecification. Moreover, we show that our proposed formulas encompass the special cases of the SB formula for CES distributions under perfect model specification, the SB formulas in the presence of misspecified Gaussian models, and the SB formula for the estimation of the scatter matrix of a set of CES distributed data under misspecification of the density generator.
AB - In this paper, Slepian-Bangs-type formulas for Complex Elliptically Symmetric distributed (CES) data vectors in the presence of model misspecification are provided. The basic Slepian-Bangs (SB) formula has been introduced in the array processing literature as a convenient and compact representation of the Fisher Information Matrix (FIM) for parameter estimation under (parametric) Gaussian data model. Extending recent results on this topic, in this paper, we provide a new generalization of the classical SB formula to parametric estimation problems involving non-Gaussian, heavy-tailed, CES distributed data in the presence of model misspecification. Moreover, we show that our proposed formulas encompass the special cases of the SB formula for CES distributions under perfect model specification, the SB formulas in the presence of misspecified Gaussian models, and the SB formula for the estimation of the scatter matrix of a set of CES distributed data under misspecification of the density generator.
KW - Complex Elliptically Symmetric distribution
KW - Mismatch
KW - Misspecified Cramér-Rao Bound
KW - Misspecified models
KW - Slepian-Bangs formula
UR - https://www.scopus.com/pages/publications/85026667110
U2 - 10.1016/j.sigpro.2017.07.029
DO - 10.1016/j.sigpro.2017.07.029
M3 - Article
AN - SCOPUS:85026667110
SN - 0165-1684
VL - 142
SP - 320
EP - 329
JO - Signal Processing
JF - Signal Processing
ER -