[R] Implementing Silverman's Negative Reflection

sreblam malbers at student.ethz.ch
Fri Sep 30 10:50:10 CEST 2011

I'm trying to implement in R in an easy way the negative reflection method
described in Silverman (1986) on p.31, ie I have a non-negative dataset and
would like to estimate the density by applying a reflection method where the
reflected points have weight -1.
I thought there should be a way to evaluate the wanted kernel at the
required points, in other words to calculate formula (2.16):
fhat(x) = 1/(nh) * sum_{i=1}^{n}{ K( (x-Xi) /h) - K( (x-Xi) /h) }

Unfortunately, I am still not that good and skilled with R - does anybody
know how to do this- Or maybe a hint...?
Thank you!!

PS: you can also find the mentioned passage on p.21 of

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