Adaptive Gaussian kernel density estimation (simplified)        [STB-16: snp6]
--------------------------------------------------------

         ^adgaker2^ varname halfwidth density midpt

Description
-----------

^adgaker2^ 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.  ^adgaker2^ 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).
To speed program execution, the density is estimated only at 50 equally
spaced points.

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 the adaptive procedure requires the calculation of a 
preliminary density estimation and individual local weights, the time 
required to complete the task is proportional to _N.  Please be patient. 

Example
-------

  . ^adgaker2 infmorat 20 adensity midpt^

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

  . ^list midpt adensity in f/50^

the values of the 50 midpoints and their corresponding estimated density 
appear on screen.

  . ^graph adensity midpt if _n<=50, xlab ylab c(s) s(o)^
 
The graphic with the density estimates and midpoints ("smoothed" histogram) 
will appear on screen. 


Authors
-------

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

References
----------

   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.


Also see
--------

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