On Bickel and Ritov's conjecture about adaptive estimation of the integral of the square of density derivative

DOI10.1214/aos/1032894459zbMath0859.62039OpenAlexW2002330520WikidataQ122872992 ScholiaQ122872992MaRDI QIDQ1816592

Sam Efromovich, Mark G. Low

Publication date: 9 April 1997

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1032894459

zbMATH Keywords

rate of convergenceasymptotic efficiencyadaptive estimatordensity estimationadaptationfunctional estimationcross validationdensity derivativesoptimal nonadaptive estimatorrate of risk convergence

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Statistical decision theory (62C99)

Related Items (7)

Estimation of quadratic functionals of a density ⋮ Fourier series-based direct plug-in bandwidth selectors for kernel density estimation ⋮ On information pooling, adaptability and superefficiency in nonparametric function estimation ⋮ Adaptive estimation of a quadratic functional of a density by model selection ⋮ Root \(n\) estimates of vectors of integrated density partial derivative functionals ⋮ On optimal adaptive estimation of a quadratic functional ⋮ On nonparametric tests of positivity/monotonicity/convexity

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• Minimax quadratic estimation of a quadratic functional
• On the estimation of quadratic functionals
• A constrained risk inequality with applications to nonparametric functional estimation
• On optimal adaptive estimation of a quadratic functional
• Approximation Theorems of Mathematical Statistics
• Nonparametric Estimation of a Density of Unknown Smoothness

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