Kernel density estimation (rectangular weight function)         [STB-16: snp6]
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         ^kernsim^ varname halfwidth density midpt

Description
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^kernsim^ estimates the density of "varname" using a rectangular weight 
function as described in Fox, (1990).  Following a suggestion of 
Chambers et. al. (1983), the density is estimated at 50 equally spaced points 
in the range of "varname".  "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.  "midpt" is a new variable 
that contains the midpoints of the 50 bins within which the density is
calculated.  The data set is assumed to be sorted in the order of "varname".

This procedure can be regarded as a descriptive smoother of histograms.
Indeed this simple density estimator is like a histogram using bins of the
specified width (2*h) but no fixed origin; the bin's windows run along the 
series with each observation at its midpoint allowing overlap.
The "smoothness" of the result can be regulated by changing the width of
the interval. Wide intervals produce smooth results; narrow intervals
result in noiser density values.

Example
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  . ^kernsim infmorat 20 density midpt^

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

  . ^list midpt density^ in 1/50

lists the values of the 50 midpoints and the estimated density at each point.

  . ^graph density midpt if _n<=50, c(l) s(p)^

displays a graph of the density estimate.


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^, ^kernepa^, ^kerngaus^, 
         ^adgakern^, ^adgaker2^