Adaptive global confidence band for nonparametric regression: An empirical likelihood method

Lixing ZHU*, Lu Lin, Qiang Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we construct adaptive global confidence bands for nonparametric regression functions by empirical likelihood (EL). First, we show that the size of the classical EL-based confidence region is not adaptive to the submodels of the function in rate-optimal way, that is, it is not model-adaptive. In contrast, the existing model-adaptive methods are not data-adaptive, that is, the shapes of the resulting confidence regions are not determined by data. Thus, we propose an EL-based method to construct model-data-adaptive global confidence bands for nonparametric regression models with some constraints. The key remark is that the size (radius) of the confidence region is not determined by the (asymptotic) distribution but by a U-statistic that is highly related to the smoothness of the submodels. The newly proposed confidence region has the model-data-adaptive property: the size adapts to the submodels in a rate-optimal way and its shape is determined by the data. Implementation issue is investigated, and simulations are carried out for illustration.

Original languageEnglish
Pages (from-to)1771-1787
Number of pages17
JournalStatistica Sinica
Volume20
Issue number4
Publication statusPublished - Oct 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Adaptability
  • Confidence region
  • Empirical likelihood
  • Nonparametric regression

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