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kosin
1999 Dec 01
1
density(kernel = "cosine") .. the `wrong cosine' ..
...x) = pi/4 * cos(pi/2 * x) * I{ |x| <= 1 }
i.e. in R
Kcos <- function(x) ifelse(abs(x) <= 1, pi/4 * cos(pi/2 * x), 0)
Now, R has instead (for bandwidth h <- bw/1.135724 which makes the bandwidth
Gaussian equivalent;
here just h == 1/pi to be similar to above)
Kcosine <- function(x) ifelse(abs(x) < 1, (1+cos(x*pi))/2 , 0)
I've looked in Dave Scott's (and Haerdle's "Smoothing... in S") book,
(Silverman doesn't mention any cosine kernel)
and both define the cosine kernel as I have it in my notes.
With above R code, look at
x...