The selection of terms in an orthogonal series density estimator

Peter J. Diggle; Peter Hall

doi:10.1080/01621459.1986.10478265

The selection of terms in an orthogonal series density estimator

Peter J. Diggle, Peter Hall

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

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 language	English (US)
Pages (from-to)	230-233
Number of pages	4
Journal	Journal of the American Statistical Association
Volume	81
Issue number	393
DOIs	https://doi.org/10.1080/01621459.1986.10478265
State	Published - 1986
Externally published	Yes

Keywords

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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10.1080/01621459.1986.10478265

Cite this

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abstract = "We show that Kronmal and Tarter{\textquoteright}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",

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AU - Hall, Peter

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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

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JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

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ER -

The selection of terms in an orthogonal series density estimator

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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