Asymptotic confidence bands for the histogram regression estimator

2025/08/17 by Neumeyer, Natalie, Rabe, Jan, Trabs, Mathias
#62G08 #62G20 #62H12 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2508.12391

Abstract

In a multivariate nonparametric regression model with a Hölder continuous regression function and heteroscedastic noise asymptotic uniform confidence bands are constructed based on the histogram estimator. The radius of the confidence bands does not depend on an extreme value distribution, but instead can be numerically calculated for the chosen binning.

Citations

• Asymptotic confidence bands for centered purely random forests
• Gaussian Approximation for Lag-Window Estimators and the Construction of Confidence bands for the Spectral Density
• Handy Formulas for Binomial Moments
• Strongly universally consistent nonparametric regression and\n classification with privatised data
• Optimal estimation of variance in nonparametric regression with random design
• Locally Adaptive Confidence Bands
• Confidence Corridors for Multivariate Generalized Quantile Regression

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