### Abstract

In this note we derive a weighted non-linear least squares procedure for choosing the smoothing parameter in a Fourier approach to deconvolution of a density estimate. The method has the advantage over a previous procedure in that it is robust to the range of frequencies over which the model is fitted. A simulation study with different parametric forms for the densities in the convolution equation demonstrates that the method can perform well in practice. A truncated form of the estimator generally has a lower mean asymptotic integrated squared error than an alternative, continuously damped form, but the damped method gives better estimates of tail probabilities.

Original language | English (US) |
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Pages (from-to) | 223-232 |

Number of pages | 10 |

Journal | Journal of Nonparametric Statistics |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1995 |

Externally published | Yes |

### Fingerprint

### Keywords

- Deconvolution
- density estimation
- Fourier transform
- smoothing

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

*Journal of Nonparametric Statistics*,

*4*(3), 223-232. https://doi.org/10.1080/10485259508832614

**Choosing the smoothing parameter in a fourier approach to nonparametric deconvolution of a density estimate.** / Barry, J.; Diggle, P.

Research output: Contribution to journal › Article

*Journal of Nonparametric Statistics*, vol. 4, no. 3, pp. 223-232. https://doi.org/10.1080/10485259508832614

}

TY - JOUR

T1 - Choosing the smoothing parameter in a fourier approach to nonparametric deconvolution of a density estimate

AU - Barry, J.

AU - Diggle, P.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - In this note we derive a weighted non-linear least squares procedure for choosing the smoothing parameter in a Fourier approach to deconvolution of a density estimate. The method has the advantage over a previous procedure in that it is robust to the range of frequencies over which the model is fitted. A simulation study with different parametric forms for the densities in the convolution equation demonstrates that the method can perform well in practice. A truncated form of the estimator generally has a lower mean asymptotic integrated squared error than an alternative, continuously damped form, but the damped method gives better estimates of tail probabilities.

AB - In this note we derive a weighted non-linear least squares procedure for choosing the smoothing parameter in a Fourier approach to deconvolution of a density estimate. The method has the advantage over a previous procedure in that it is robust to the range of frequencies over which the model is fitted. A simulation study with different parametric forms for the densities in the convolution equation demonstrates that the method can perform well in practice. A truncated form of the estimator generally has a lower mean asymptotic integrated squared error than an alternative, continuously damped form, but the damped method gives better estimates of tail probabilities.

KW - Deconvolution

KW - density estimation

KW - Fourier transform

KW - smoothing

UR - http://www.scopus.com/inward/record.url?scp=0041691699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041691699&partnerID=8YFLogxK

U2 - 10.1080/10485259508832614

DO - 10.1080/10485259508832614

M3 - Article

VL - 4

SP - 223

EP - 232

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 3

ER -