Wavelet methods to estimate an integrated quadratic functional: Adaptivity and asymptotic law

DOI10.1016/S0167-7152(98)00296-XzbMath0947.62029MaRDI QIDQ1962183

Karine Tribouley, Ghislaine Gayraud

Publication date: 30 January 2000

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

zbMATH Keywords

adaptive estimationminimax riskconfidence bandswavelet thresholding methods

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

Related Items (12)

Sharp adaptive estimation of quadratic functionals ⋮ Optimal adaptive estimation of a quadratic functional ⋮ Integrated volatility and round-off error ⋮ A Bernstein-von Mises theorem for smooth functionals in semiparametric models ⋮ On adaptive wavelet estimation of a quadratic functional from a deconvolution problem ⋮ Estimating linear and quadratic forms via indirect observations ⋮ OPTIMAL TESTING IN A FIXED-EFFECTS FUNCTIONAL ANALYSIS OF VARIANCE MODEL ⋮ OPTIMAL TESTING IN A FIXED-EFFECTS FUNCTIONAL ANALYSIS OF VARIANCE MODEL ⋮ Estimation of the Hurst parameter from discrete noisy data ⋮ Adaptive estimation of a quadratic functional of a density by model selection ⋮ Rate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problems ⋮ Adaptive estimation of a quadratic functional by model selection.

Cites Work

• Minimax quadratic estimation of a quadratic functional
• On the estimation of quadratic functionals
• On optimal adaptive estimation of a quadratic functional
• Adaptive confidence interval for pointwise curve estimation.
• Estimation of integral functionals of a density
• Some Problems on Nonparametric Estimation in Gaussian White Noise
• Ten Lectures on Wavelets
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