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A nonparametric Cramér–Rao inequality for estimators of statistical functionals

✍ Scribed by Arnold Janssen

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
269 KB
Volume
64
Category
Article
ISSN
0167-7152

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✦ Synopsis

The present paper introduces a lower bound for the mean quadratic error of estimators of di erentiable statistical functionals. The result can be extended to bilinear covariance forms of vector-valued estimators. The lower bound leads to a concept of Fisher e ciency of estimators for functionals. The concept is based on tangent spaces and L 2 -di erentiable submodels.

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✍ S Cavassila; S Deval; C Huegen; D van Ormondt; D Graveron-Demilly 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 180 KB

We have derived analytical expressions of the Cramer-Rao lower bounds on spectral parameters for singlet, doublet, and triplet peaks in noise. We considered exponential damping (Lorentzian lineshape) and white Gaussian noise. The expressions, valid if a sufficiently large number of samples is used,