Adaptive Gaussian kernel density estimation                     [STB-16: snp6]
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         ^adgakern^ varname halfwidth density 

Description
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^adgakern^ estimates the density of "varname" using the adaptive Gaussian 
kernel described in Fox (1990) modified from Silverman (1986).  "halfwidth"
is a constant that specifies the width of the density window around each
point.  "density" is a new variable that contains the density estimate on 
output.  ^adgakern^ estimates densities using a Gaussian kernel with fixed 
window, then uses these estimates to determine local weights inversely 
proportional to the preliminary density estimate.  These local weights are 
used to adjust the window width so that it is narrower at high densities 
(retaining detail) and wider where density is low (eliminating noise).

As with the fixed window kernels the "smoothness" of the result can be 
regulated by changing the width of the interval (i.e. varying 'h'). Wide 
intervals produce smooth results; narrow intervals will result in noiser 
density values.

WARNING: Because this implementation requires the calculation of local 
weights for each individual observation based on a preliminary density 
estimation, the time required is proportional to 2*_N.  Please be patient. 

Example
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  . ^adgakern infmorat 20 adensity^

After some time (depending on the number of observations) the results are
placed in the new variable ^adensity^. 

  . ^list infmorat adensity^

the values of the original variable and their corresponding estimated density 
appear on screen. 

  . ^graph adensity infmorat, xlab ylab c(s) s(.)^
 
The graphic with the density estimates for each original value ("smoothed" 
histogram) will appear on screen. You can combine this with the oneway and 
box options.


References
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   Chambers, J.M., W.S. Cleveland, B. Kleiner and P.A. Tukey (1983)
        Graphical Methods for Data Analysis. Wadsworth & Brooks/Cole
        Chap. 2: 9-46.
   Silverman, B.W. (1986) Density Estimation for Statistics and Data 
	Analysis. Chapman and Hall.
   Fox, J. (1990) Describing univariate distributions. In (Fox, J. &
        J.S. Long, Eds.) "Modern Methods of Data Analysis". Sage
        Chap. 2: 58-125.


Authors
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Isaias H. Salgado-Ugarte, Makoto Shimizu and Toru Taniuchi
University of Tokyo, Faculty of Agriculture,
Dept. of Fisheries (Fax 81-3-3812-0529)


Also see
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    STB: snp6 (STB-16)
On-line: ^help^ for ^boxdetra^, ^boxdetr2^, ^cosdetra^, ^kernsim^, ^kernepa^, 
         ^kerngaus^, ^adgaker2^