The selection of terms in an orthogonal series density estimator

Peter J. Diggle, Peter Hall

Research output: Contribution to journalArticle


We show that Kronmal and Tarter’s well-known rule for selecting the terms in an orthogonal series density estimator can lead to poor performance and even inconsistency in certain cases. These difficulties arise when the underlying density has a nonmonotone sequence of Fourier coefficients, as is likely to be the case with sharply peaked or multimodal distributions. We suggest a way of overcoming these shortcomings.

Original languageEnglish (US)
Pages (from-to)230-233
Number of pages4
JournalJournal of the American Statistical Association
Issue number393
Publication statusPublished - 1986
Externally publishedYes



  • Kronmal and tarter
  • Mode
  • Nonparametric density estimation
  • Number of terms
  • Trigonometric series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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