[R] Problem with density()?

[Thomas Lumley]

On Thu, 10 Aug 2000, Nels Tomlinson wrote:

> Hello, all,
> 
> I'm running Version 1.1.0  (June 15, 2000), on Mandrake 6.1 Linux.  
> 
> I think that I'm getting nonsense results from the density function. 
> When I feed it a sample generated by v<-runif(1000,0,1), I get back some
> small negative numbers for density values, as follows:
> 

If you do 
   slime$x[slime$y<0] 
I think you will find that the negative values happen at x values outside
the range of the data. When I tried they were all <-0.1 or >1.1, with a
bandwidth of 0.065.  As the density really is zero here it's not
surprising that the estimate is effectively zero. (It's not a bug, it's a
feature)

It is unfortunate, I suppose, that the density is slightly negative rather
than slightly positive, but it wouldn't make much practical difference to
your problem: you don't want to divide by it anyway. 

With the obvious implementation of kernel densities the estimate would
have to be non-negative even with rounding error, and would be zero or NaN
at these points.  However, the FFT implementation is way faster.
	
	-thomas

> 
> >v<-runif(1000,0,1)
> > dump("v","/home/tomlinso/auction/test.vector.R")
> > slime<-density(v,kernel="r")
> > sort(slime$y)
>   [1] -1.869303e-16 -1.110223e-16 -1.110223e-16 -1.065198e-16
> -1.057452e-16
>   [6] -1.016304e-16 -9.779196e-17 -9.427232e-17 -9.368320e-17
> -8.471147e-17
>  [11] -8.169144e-17 -7.225386e-17 -6.740389e-17 -6.142515e-17
> -6.003374e-17
>  [16] -5.652376e-17 -5.501082e-17 -5.348798e-17 -5.347797e-17
> -5.319815e-17
>  [21] -5.043385e-17 -4.948219e-17 -4.835455e-17 -4.633728e-17
> -4.466063e-17
>  [26] -4.039872e-17 -3.836554e-17 -3.826879e-17 -3.646713e-17
> -3.557390e-17
>  [31] -2.825989e-17 -2.821749e-17 -2.743282e-17 -2.678935e-17
> -2.533472e-17
>  [36] -2.518910e-17 -2.510075e-17 -2.436936e-17 -1.919740e-17
> -1.831052e-17
>  [41] -1.757412e-17 -1.673804e-17 -1.615867e-17 -1.327275e-17
> -1.318810e-17
>  [46] -1.286342e-17 -9.888095e-18 -8.665413e-18 -6.783308e-18
> -5.726469e-18
>  [51] -2.394122e-19  7.552237e-18  1.063422e-17  2.765485e-17 
> 3.848034e-17
>  [56]  4.637632e-17  4.727742e-17  6.705682e-17  6.914125e-17 
> 8.924077e-17
>  [61]  6.663715e-04  1.703646e-03  3.401654e-03  8.696669e-03 
> 1.349002e-02
>  [66]  1.861714e-02  2.548490e-02  2.719238e-02  3.502090e-02 
> 3.752716e-02
> <snip>
> 
> I don't think that I should be getting negative numbers, even tiny
> ones.  These are close enough to zero to cause trouble, since the
> estimator I'm implementing calls for dividing by those density values!  
> 
> Any clues about what hit me and what I can do about it would be
> appreciated.  
> 
> Thanks,
> Nels Tomlinson
> -- 
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> 

Thomas Lumley
Assistant Professor, Biostatistics
University of Washington, Seattle

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