On automatic boundary corrections

Ming Yen Cheng, Jianqing Fan, J. S. Marron

Research output: Contribution to journalArticlepeer-review

168 Scopus citations


Many popular curve estimators based on smoothing have difficulties caused by boundary effects. These effects are visually disturbing in practice and can play a dominant role in theoretical analysis. Local polynomial regression smoothers are known to correct boundary effects automatically. Some analogs are implemented for density estimation and the resulting estimators also achieve automatic boundary corrections. In both settings of density and regression estimation, we investigate best weight functions for local polynomial fitting at the endpoints and find a simple solution. The solution is universal for general degree of local polynomial fitting and general order of estimated derivative. Furthermore, such local polynomial estimators are best among all linear estimators in a weak minimax sense, and they are highly efficient even in the usual linear minimax sense.

Original languageEnglish (US)
Pages (from-to)1691-1708
Number of pages18
JournalAnnals of Statistics
Issue number4
StatePublished - Aug 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Boundary correction
  • Data binning
  • Local polynomial fit
  • Minimax risk
  • Weak minimaxity


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