Some problems on the estimation of unimodal densities

Peter J. Bickel, Jianqing Fan

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


In this paper, we study, in some new ways, the estimation of unimodal densities. Several methods for estimating unimodal densities are proposed: plug-in MLE, pregrouping techniques, linear spline MLE. Based on the maximum likelihood method, an automatic procedure for estimating a unimodal density as well as its mode is proposed. We also give asymptotic theory for the proposed estimators. An important consequence of this study is that having to estimate the location of a mode does not affect the limiting behavior of the proposed unimodal density estimate. Simulation studies illustrate the proposed methods.

Original languageEnglish (US)
Pages (from-to)23-45
Number of pages23
JournalStatistica Sinica
Issue number1
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Asymptotic distributions
  • MLE
  • Modes
  • Plug-in methods
  • Pregrouping methods
  • Unimodal densities


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