Hello,
My friend has the following issue with R. I will be glad to receive any
response.
Thanks,
Dhiman Bhadra

Hello everyone,

I am trying to use the 'density' function available with the base package
of R to estimate the density of a data set for subsequent use. I just
noticed that with even 1000 data points, the numerical integral of the
estimated density using the Epanechnikov kernel is far from 1. I wonder if
I am doing something wrong, or whether there is a bug:

x=rnorm(10000)
> dd=density(x,kernel="epanechnikov",n=101,bw=0.001)
> sum(dd$y)*(dd$x[2]-dd$x[1])
[1] 5.7245

> dd=density(x,kernel="epanechnikov",n=1001,bw=0.001)
> sum(dd$y)*(dd$x[2]-dd$x[1])
[1] 2.870922

> dd=density(x,kernel="epanechnikov",n=10001,bw=0.001)
> sum(dd$y)*(dd$x[2]-dd$x[1])
[1] 0.9989762

So unless I use around 10000 or more data points, the integral is wrong:
there seems to be a scaling factor creeping in. Am I missing something?


Best regards,
*Apratim Guha*

__________________________________________________________________________
*Dr. Apratim Guha*
*Associate Professor, Production & Quantitative Methods Area, IIM
Ahmedabad, *

*Vastrapur, Ahmedabad 380015, INDIA. Phone: (91) 79 6632 4803*
*Secretary: Ms. Sujatha Jayprakash: (91) 79 6632 4911*

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