sm.density
Nonparametric density estimation in one, two or three dimensions.
This function creates a density estimate from data in one, two or three dimensions. In two dimensions a variety of graphical displays can be selected, and in three dimensions a contour surface can be plotted. A number of other features of the construction of the estimate, and of its display, can be controlled.
If the rpanel
package is available, an interactive panel can be
activated to control various features of the plot.
If the rgl
package is also available, rotatable plots are
available for the two and threedimensional cases. (For
threedimensional data, the misc3d
package is also required.)
 Keywords
 smooth, nonparametric
Usage
sm.density(x, h, model = "none", weights = NA, group=NA, ...)
Arguments
 x
 a vector, or a matrix with two or three columns, containing the data.
 h
 a vector of length one, two or three, defining the smoothing parameter.
A normal kernel function is used and
h
is its standard deviation. If this parameter is omitted, a normal optimal smoothing parameter is used.  model
 This argument applies only with onedimensional data. Its default value
is
"none"
. If it is set to"Normal"
(or indeed any value other than"none"
) then a reference band, indicating where a density estimate is likely to lie when the data are normally distributed, will be superimposed on any plot.  weights
 a vector of integers representing frequencies of individual observations.
Use of this parameter is incompatible with binning; hence
nbins
must then be set to 0 or left at its default valueNA
.  group
 a vector of groups indicators (numeric or character values) or a factor.
 ...

other optional parameters are passed to the
sm.options
function, through a mechanism which limits their effect only to this call of the function. Those specifically relevant for this function are the following:hmult
,h.weights
,band
,add
,lty
,display
,props
,xlab
,ylab
,zlab
,xlim
,ylim
,yht
,nbins
,ngrid
,eval.points
,panel
,positive
,delta
,theta
,phi
; see the documentation ofsm.options
for their description.
Details
see Chapters 1, 2 and 6 of the reference below.
In the threedimensional case, the contours of the density estimate are
constructed by the contour3d
function in the misc3d
package of Feng & Tierney.
Value

a list containing the values of the density estimate at the evaluation points,
the smoothing parameter, the smoothing parameter weights and the kernel
weights. For one and twodimensional data, the standard error of the estimate
(on the square root scale, where the standard error is approximately constant)
and the upper and lower ends of a variability band are also supplied. Less
information is supplied when the smoothing parameter weights
or kernel weights are not all 1, or when
positive
is set to TRUE
.
Side Effects
a plot is produced, unless the option display="none"
is set.
References
Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with SPlus Illustrations. Oxford University Press, Oxford.
See Also
h.select
, hnorm
, hsj
, hcv
,
nise
, nmise
, sm
,
sm.sphere
, sm.regression
,
sm.options
Examples
library(sm)
# A onedimensional example
y < rnorm(50)
sm.density(y, model = "Normal")
# sm.density(y, panel = TRUE)
# A twodimensional example
y < cbind(rnorm(50), rnorm(50))
sm.density(y, display = "image")
# sm.density(y, panel = TRUE)
# A threedimensional example
# y < cbind(rnorm(50), rnorm(50), rnorm(50))
# sm.density(y)