Peter Hall's contributions to nonparametric function estimation and modeling

Ming Yen Cheng, Jianqing Fan

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Peter Hall made wide-ranging and far-reaching contributions to nonparametric modeling. He was one of the leading figures in the developments of nonparametric techniques with over 300 published papers in the field alone. This article gives a selective overview on the contributions of Peter Hall to nonparametric function estimation and modeling. The focuses are on density estimation, nonparametric regression, bandwidth selection, boundary corrections, inference under shape constraints, estimation of residual variances, analysis of wavelet estimators, multivariate regression and applications of nonparametric methods.

Original languageEnglish (US)
Pages (from-to)1837-1853
Number of pages17
JournalAnnals of Statistics
Issue number5
StatePublished - Oct 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Bandwidth
  • Boundary
  • Cross-validation
  • Density
  • Edge
  • Endpoints
  • Exponent
  • Fractal
  • Local linear
  • Mode estimator
  • Nonparametric
  • Projection pursuit
  • Regression
  • Smoothing parameter
  • Tilting
  • Trigonometric
  • Variance function


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