Bootstrap confidence bands for regression curves and their derivatives
Open Access
- 1 December 2003
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 31 (6), 1852-1884
- https://doi.org/10.1214/aos/1074290329
Abstract
Confidence bands for regression curves and their first p derivatives are obtained via local pth order polynomial estimation. The method allows for multiparameter local likelihood estimation as well as other unbiased estimating equations. As an alternative to the confidence bands obtained by asymptotic distribution theory, we also study smoothed bootstrap confidence bands. Simulations illustrate the finite sample properties of the methodology.Keywords
This publication has 36 references indexed in Scilit:
- Local Estimating EquationsJournal of the American Statistical Association, 1998
- Simultaneous bootstrap confidence bands in nonparametric regressionJournal of Nonparametric Statistics, 1998
- Local Polynomial Kernel Regression for Generalized Linear Models and Quasi-Likelihood FunctionsJournal of the American Statistical Association, 1995
- Asymptotics of kernel estimators based on local maximum likelihoodJournal of Nonparametric Statistics, 1994
- Confidence Bands in Nonparametric RegressionJournal of the American Statistical Association, 1993
- Design-adaptive Nonparametric RegressionJournal of the American Statistical Association, 1992
- On convergence rates of supremaProbability Theory and Related Fields, 1991
- The Kernel Estimate of a Regression Function in Likelihood-Based ModelsJournal of the American Statistical Association, 1989
- Confidence Bands for Regression FunctionsJournal of the American Statistical Association, 1985
- Robust Locally Weighted Regression and Smoothing ScatterplotsJournal of the American Statistical Association, 1979