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

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