On confidence bands for multivariate nonparametric regression

Katharina Proksch*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

In a multivariate nonparametric regression problem with fixed, deterministic design asymptotic, uniform confidence bands for the regression function are constructed. The construction of the bands is based on the asymptotic distribution of the maximal deviation between a suitable nonparametric estimator and the true regression function which is derived by multivariate strong approximation methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing system of sets. The results are derived for a general class of estimators which includes local polynomial estimators as a special case. The finite sample properties of the proposed asymptotic bands are investigated by means of a small simulation study.

Original languageEnglish
Pages (from-to)209-236
Number of pages28
JournalAnnals of the Institute of Statistical Mathematics
Volume68
Issue number1
DOIs
Publication statusPublished - 1 Feb 2016
Externally publishedYes

Keywords

  • Confidence bands
  • Multivariate regression
  • Nonparametric regression
  • Rates of convergence
  • Uniform convergence

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