A nonparametric Cramér-Rao inequality for estimators of statistical functionals.

DOI10.1016/S0167-7152(03)00179-2zbMath1116.62334MaRDI QIDQ1423107

Arnold Janssen

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

efficiencyFisherCramér--Rao inequalityDifferentiable statistical functionalsEfficient estimatorsMean quadratic error of estimators

Mathematics Subject Classification ID

Nonparametric estimation (62G05)

Related Items (4)

Information bounds for nonparametric estimators of \(L\)-functionals and survival functionals under censored data ⋮ Variance bounds for estimators in autoregressive models with constraints ⋮ Natural differentiable structures on statistical models and the Fisher metric ⋮ Cramér-Rao revisited

Cites Work

• On the attainment of the Cramér-Rao bound in \({\mathbb{L}}_ r\)- differentiable families of distributions
• Contributions to a general asymptotic statistical theory. With the assistance of W. Wefelmeyer
• Mathematical theory of statistics. Statistical experiments and asymptotic decision theory
• Unbiased estimation of von Mises functionals
• Characterization of the law of the iterated logarithm in Banach spaces
• Testing nonparametric statistical functionals with applications to rank tests
• Applications of the van Trees inequality: A Bayesian Cramér-Rao bound
• A nonparametric asymptotic version of the Cramér-Rao bound
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