Some nonasymptotic bounds for \(L_ 1\) density estimation using kernels

DOI10.1214/aos/1176348791zbMath0782.62041OpenAlexW2044214282MaRDI QIDQ1206735

Somnath Datta

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1214/aos/1176348791

zbMATH Keywords

total variationkernel estimatorsminimax riskmonotone densitiesL1 estimationdensities of bounded variationL1 errornonasymptotic bounduniform upper bounds

Mathematics Subject Classification ID

Density estimation (62G07) Minimax procedures in statistical decision theory (62C20)

Related Items (5)

A bound on the \(\mathcal{L}_ 1\)-error of a nonparametric density estimator with censored data ⋮ A minimax optimal estimator for continuous monotone densities ⋮ Uniform \(L_1\)-distance large deviations in nonparametric density estimation ⋮ On the integral modulus of continuity of infinitely divisible distributions, especially of stochastic integrals ⋮ Inequalities and bounds for kernel length-biased density estimation

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