[R-sig-Geo] Negative mse values

[Rolf Turner]

On 27/03/17 21:28, Cenk İÇÖZ via R-sig-Geo wrote:

> Hi  dear friends.
>
> I was trying to smooth a spatial point pattern with kernel function
> but I am a bit confused .
> I need some explanation about negative MSE values obtained ( used
> forselecting optimum bandwidth) by using mse2d function of "splancs " package.
> As the definition of mse function for one dimension I know it might
> not take negative values.
> However I have no idea for the two dimensional definition of mse for
> aspatial point pattern. Could the mse values be negative in this case? I
> found an example taking minimum negative value of mse fort he optimum
> bandwidth which is the lowest negative value

The short answer is that the value returned by mse2d() is not actually 
the MSE but rather MSE minus a data dependent constant.  So this can 
"legitimately" be negative.

The off-setting constant "does no harm" since interest lies in 
determining the optimum bandwidth, so it is the relative sizes of the 
values produced that are of interest.

It has been suggested to me in the past (by Barry Rowlingson, one of the 
original authors of splancs) that the function bw.diggle() from the 
spatstat package may be more reliable than mse2d().  The former function 
uses a somewhat different calculation procedure, whence the results of 
the two functions are not exactly comparable.

Note that bw.diggle() is expressed in terms of "sigma" whereas mse2d()
is expressed in terms of "h" where sigma = h/2. So if mse2d() gives an
"optimal" value of 3, one would *roughly* expect bw.diggle() to give an 
optimal value of 1.5.

Note also that estimating an "optimal" bandwidth is a pretty inexact 
endeavour under the best of circumstances.  The smooth surface to be 
fitted is an ill-determined creature and the bandwidth that gives the 
best fit is even more ill-determined.

cheers,

Rolf Turner

-- 
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276