Local asymptotics for regression splines and confidence regions

S. Zhou, X. Shen, D. A. Wolfe

Research output: Contribution to journalArticlepeer-review

159 Scopus citations

Abstract

In this paper, we study the local behavior of regression splines. In particular, explicit expressions for the asymptotic pointwise bias and variance of regression splines are obtained. In addition, asymptotic normality for regression splines is established, leading to the construction of approximate confidence intervals and confidence bands for the regression function.

Original languageEnglish (US)
Pages (from-to)1760-1782
Number of pages23
JournalAnnals of Statistics
Volume26
Issue number5
DOIs
StatePublished - Oct 1998
Externally publishedYes

Keywords

  • Asymptotic bias
  • Asymptotic normality
  • Asymptotic variance
  • Bernoulli polynomial
  • Confidence interval and confidence band
  • Least squares
  • Regression splines

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