TY - JOUR

T1 - Choosing the smoothing parameter in a Fourier approach to non-parametric deconvolution of a density estimate.

AU - Barry, J.

AU - Diggle, Peter J.

PY - 1995

Y1 - 1995

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

U2 - 10.1080/10485259508832614

DO - 10.1080/10485259508832614

M3 - Journal article

VL - 4

SP - 223

EP - 232

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 3

ER -