Estimating nonquadratic functionals of a density using Haar wavelets

DOI10.1214/aos/1032894450zbMath0860.62033OpenAlexW1981648336MaRDI QIDQ1816599

Gérard Kerkyacharian, Dominique Picard

Publication date: 27 November 1996

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

Full work available at URL: https://doi.org/10.1214/aos/1032894450

zbMATH Keywords

rate of convergenceBesov spacesTaylor expansionminimax estimationU-statisticHaar basiswavelet estimateestimation of nonlinear functionalsintegral functionals of densities

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40)

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Cites Work

• Achieving information bounds in non and semiparametric models
• Minimax quadratic estimation of a quadratic functional
• Estimation of integrated squared density derivatives
• Optimal plug-in estimators for nonparametric functional estimation
• Density estimation by kernel and wavelets methods: optimality of Besov spaces
• Efficient estimation of integral functionals of a density
• Estimation of integral functionals of a density
• On Necessary Conditions for Efficient Estimation of Functionals of a Nonparametric Signal in White Noise
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