The selection of terms in an orthogonal series density estimator

Peter J. Diggle, Peter Hall

Research output: Contribution to journalArticle

Abstract

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
Volume81
Issue number393
DOIs
StatePublished - 1986
Externally publishedYes

Fingerprint

Orthogonal Series
Density Estimator
Fourier coefficients
Inconsistency
Likely
Term
Estimator
Coefficients

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

The selection of terms in an orthogonal series density estimator. / Diggle, Peter J.; Hall, Peter.

In: Journal of the American Statistical Association, Vol. 81, No. 393, 1986, p. 230-233.

Research output: Contribution to journalArticle

Diggle, Peter J. ; Hall, Peter. / The selection of terms in an orthogonal series density estimator. In: Journal of the American Statistical Association. 1986 ; Vol. 81, No. 393. pp. 230-233.
@article{bf5bfefca6264f979d90a9b4eed74333,
title = "The selection of terms in an orthogonal series density estimator",
abstract = "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.",
keywords = "Kronmal and tarter, Mode, Nonparametric density estimation, Number of terms, Trigonometric series",
author = "Diggle, {Peter J.} and Peter Hall",
year = "1986",
doi = "10.1080/01621459.1986.10478265",
language = "English (US)",
volume = "81",
pages = "230--233",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "393",

}

TY - JOUR

T1 - The selection of terms in an orthogonal series density estimator

AU - Diggle, Peter J.

AU - Hall, Peter

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

KW - Kronmal and tarter

KW - Mode

KW - Nonparametric density estimation

KW - Number of terms

KW - Trigonometric series

UR - http://www.scopus.com/inward/record.url?scp=0010950787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010950787&partnerID=8YFLogxK

U2 - 10.1080/01621459.1986.10478265

DO - 10.1080/01621459.1986.10478265

M3 - Article

AN - SCOPUS:0010950787

VL - 81

SP - 230

EP - 233

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 393

ER -