Estimation of a distribution from data with small measurement errors

DOI10.1214/13-EJS850zbMath1293.62068OpenAlexW1984066234MaRDI QIDQ372132

Michael Kohler, Ann-Kathrin Bott, Luc P. Devroye

Publication date: 14 October 2013

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

Full work available at URL: https://projecteuclid.org/euclid.ejs/1380719362

zbMATH Keywords

density estimationnonparametric regressionresidualsmeasurement errorsdistribution estimationuniversal consistency\(L_{1}\) errortotal variation error

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items

Estimation of conditional distribution functions from data with additional errors applied to shape optimization, Data depth for measurable noisy random functions, Rothman-Woodroofe symmetry test statistic revisited, Improved density and distribution function estimation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L_1\)-consistent estimation of the density of residuals in random design regression models
• Strongly consistent density estimation of the regression residual
• No empirical probability measure can converge in the total variation sense for all distributions
• Deconvolution problems in nonparametric statistics
• Estimating the error distribution in nonparametric multiple regression with applications to model testing
• The equivalence of weak, strong, and complete convergence in \(L_ 1\) for kernel density estimates
• Distribution-free consistency results in nonparametric discrimination and regression function estimation
• The empirical distribution function of residuals from generalised regression
• Residuals density estimation in nonparametric regression
• Consistent nonparametric regression. Discussion
• Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression
• A distribution-free theory of nonparametric regression
• Consistency of error density and distribution function estimators in nonparametric regression.
• Probability essentials
• Estimation of the density of regression errors
• Optimal nonparametric estimation of the density of regression errors with finite support
• Weak convergence of the sample distribution function when parameters are estimated
• Non-parametric Estimation of the Residual Distribution
• Estimation of a Density Using Real and Artificial Data
• Remarks on Some Nonparametric Estimates of a Density Function
• Nonparametric regression estimation using penalized least squares
• Nonparametric estimation via empirical risk minimization
• Rate of convergence of the density estimation of regression residual
• On Estimation of a Probability Density Function and Mode
• Combinatorial methods in density estimation