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    <p>There are several problems in your post. First: In nonparametric deconvolution problems you usually do not 'know' the distribution of 'y'. Rather you have a sample of 'y' that you assume observed with an additive noise, 'x' is unobserved. No assumptions are made on 'y' or 'x' but only on 'noise'. Your presentation seems to imply that you are considering a parametric problem (for which neither deamer or decon are of any help). Second: be careful, you are considering a non-centered noise...which deamer can deal with but not decon. Here is an example of code:</p> <pre><code>library(decon) # for DeconPdf library(deamer) # for deamerKE set.seed(12345) shape=5; scale=1; mu=0; sd=0.2 x &lt;- rweibull(5000, shape=shape, scale=scale) noise &lt;- rnorm(5000, mean=mu, sd=sd) y=x+noise curve(dweibull(x,shape,scale),lwd=2, from = 0, to = 2) est &lt;- deamerKE(y, noise.type="Gaussian", mu=mu, sigma=sd, from=0, to=2) lines(est) estDecon &lt;- DeconPdf(y, sd, error="normal", fft=TRUE) lines(estDecon, lty=2) legend('topright', lty=c(1,1,2), lwd=c(2,1,1), legend=c("true", "deamerKE", "DeconPdf")) </code></pre> <p>As you see from the plot, even with a centered noise (mu=0 in my example), the estimate is better with deamer: this is because of adaptive estimation. You could probably obtain similar results with decon though, but you would have to tune the bandwidth parameter using the functions provided for that in the package. Regarding the parameters you gave, the Fourier transforms are extremely "flat". This makes it very difficult for any all-purpose implementation to select an appropriate bandwidth parameter (either adaptively as in deamer or using an estimation as in decon). Playing around with the bandwidth parameter in deconPdf doesn't help either, probably because of numeric limits. Your problem would require some fine tuning in the deamer functions' code to allow exploration of larger collections of models. This would also dramatically increase estimation time. Could you should rather consider re-parametrizing your problem in some way?</p> <p>Best, Julien Stirnemann</p>
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