Inequalities for uniform deviations of averages from expectations with applications to nonparametric regression

DOI10.1016/S0378-3758(99)00215-3zbMath0982.62035OpenAlexW1988850203MaRDI QIDQ1582357

Michael Kohler

Publication date: 7 April 2002

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-3758(99)00215-3

zbMATH Keywords

rate of convergencepolynomial splinesleast squarescomplexity regularizationregression estimateuniform laws of large numbers

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20)

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Cites Work

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• Probability inequalities for empirical processes and a law of the iterated logarithm
• Distribution-free consistency results in nonparametric discrimination and regression function estimation
• Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz
• Decision theoretic generalizations of the PAC model for neural net and other learning applications
• Consistent nonparametric regression. Discussion
• A practical guide to splines
• Nonparametric estimation of piecewise smooth regression functions
• Risk bounds for model selection via penalization
• Sharper bounds for Gaussian and empirical processes
• The use of polynomial splines and their tensor products in multivariate function estimation. (With discussion)
• Projection estimation in multiple regression with application to functional ANOVA models
• Optimal global rates of convergence for nonparametric regression
• Lower bounds on the rate of convergence of nonparametric regression estimates
• Model selection for regression on a random design
• Efficient agnostic learning of neural networks with bounded fan-in
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Convergence of stochastic processes
• Nonparametric regression function estimation using interaction least squares splines and complexity regularization.