Density estimation with contamination: minimax rates and theory of adaptation

DOI10.1214/19-EJS1617zbMath1429.62130arXiv1712.07801OpenAlexW2978960053MaRDI QIDQ2326068

Haoyang Liu, Chao Gao

Publication date: 4 October 2019

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07801

zbMATH Keywords

adaptive estimationrobust statisticscontamination modelminimax rateLepski's methodnonparametric functional estimation

Mathematics Subject Classification ID

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

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Cites Work

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• Nonparametric density estimation for symmetric distributions by contaminated data
• A general decision theory for Huber's \(\epsilon\)-contamination model
• Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing
• Optimal adaptive estimation of a quadratic functional
• Geometrizing rates of convergence. III
• Statistical estimation and optimal recovery
• A constrained risk inequality with applications to nonparametric functional estimation
• Optimal pointwise adaptive methods in nonparametric estimation
• Deconvolving multidimensional density from partially contaminated observations
• Oracle inequalities and adaptive estimation in the convolution structure density model
• Robust covariance and scatter matrix estimation under Huber's contamination model
• Adaptive estimation of integrated functionals
• Deconvolving a density from partially contaminated observations
• Robust regression via mutivariate regression depth
• On adaptive estimation of linear functionals
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Asymptotically Minimax Adaptive Estimation. II. Schemes without Optimal Adaptation: Adaptive Estimators
• On a Problem of Adaptive Estimation in Gaussian White Noise
• Estimating the Null and the Proportion of Nonnull Effects in Large-Scale Multiple Comparisons
• Chi-square oracle inequalities
• Large-Scale Simultaneous Hypothesis Testing
• Robust Estimation of a Location Parameter
• A Robust Version of the Probability Ratio Test
• Introduction to nonparametric estimation
• Combinatorial methods in density estimation