sm.density: Nonparametric density estimation in one, two or three dimensions.

Description

This function creates a density estimate from data in one, two or three dimensions. In one dimension, an interactive panel can be activated to control the smoothing parameter, 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.

Usage

sm.density(x, h, model = "none", weights=rep(1,nobs), ...)

Arguments

a vector, or a matrix with two or three columns, containing the data.

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 one-dimensional 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 lik

weights

a vector which allows the kernel functions over the observations to take different weights when they are averaged to produce a density estimate. Use of this parameter is incompatible with binning; hence nbins must then be set to 0 or left at

...

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 relevant for this function are the following:

hmult

a factor which can be used to multiply the normal smoothing parameter before construction of the density estimate.

h.weights

a vector of weights which multiply the smoothing parameter used in the kernel function at each observation. This argument does not apply with three-dimensional data.

band

a logical value which controls whether the reference band appears on the plot. Its default value is TRUE. This argument applies only with one-dimensional data.

add

a logical value which controls whether the density estimate is added to the current plot. Its default value is FALSE, which creates a new plot. This argument applies only with one-dimensional data.

lty

the line type used to plot the density estimate. This argument applies only with one-dimensional data.

display

This argument applies only with one- or two-dimensional data. The setting "none" will prevent any graphical output from being produced. In one dimensions, the default setting "estimate" will produce the density estimate, while

props

a vector defining the proportions of the data to be included within each contour in a slice plot, from two-dimensional data, or a contour surface plot, from three-dimensional data. In the three-dimensional case only the first element of the vector will b

xlab

the label attached to the x-axis.

ylab

the label attached to the y-axis.

zlab

the label attached to the z-axis (three-dimensional plots only)

xlim

the range of the horizontal axis of the plot. This argument does not apply with three-dimensional data.

ylim

the range of the vertical axis of the plot. This argument does not apply with three-dimensional data.

yht

the upper limit of the vertical axis in a plot of a one-dimensional density estimate. The lower limit is always set to 0. This argument does not apply with two- or three-dimensional data.

nbins

The number of bins used in one-dimensional binning operations; in two-dimensional cases, nbins refers to the number of bins formed along each axis. Bins with 0 observed frequencies are ignored. If nbins=0, binning is not perform

ngrid

the number of points in the regular grid used to plot the estimate. For two- and three-dimensional data, ngrid refers to the number of points along the axis in each dimension. Default: 100, 50 and 20 for 1-, 2- and 3-dimensional data, respec

eval.points

the points at which the density estimate should be evaluated, for the values returned in the result of the function. This should be a vector for one-dimensional data and a two-column matrix for two-dimensional data. This argument does not apply with thre

panel

a logical value which controls the appearance of a panel display, in the case of one- or two-dimensional data. The panel can be used to alter the value of the smoothing parameter. For one-dimensional data it can also launch an animation, and superimpose

positive

a logical value which indicates whether the data should be assumed to take positive values only. When this argument is set to TRUE, a log transformation is applied to the data before construction of a density estimate. The result is transfo

delta

a value which will be added to the data before they are log transformed in the procedure to handle positive data. The value of delta is used only when positive takes the value TRUE. The default value is the smalles

theta

the horizontal rotation (in radians) of the contour plot of the density estimate from three-dimensional data. The default value is $\pi/4$.

phi

the vertical rotation (in radians) of the contour plot of the density estimate from three-dimensional data. The default value is $\pi/4$.

Value

a list containing the values of the density estimate at the evaluation points, the standard error of the estimate, the upper and lower ends of a variability band, the smoothing parameter, the smoothing parameter weights and the kernel weights. 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 on the current graphical device is produced, unless display="none".

Details

see Chapters 1, 2 and 6 of the reference below. The code for drawing contours of a three-dimensional density estimate has been amended from an original function written by Stuart Young.

References

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.

Examples

Run this code

#  A one-dimensional example
y <- rnorm(50)
sm.density(y, model = "Normal")


#  A two-dimensional example
y <- cbind(rnorm(50), rnorm(50))
sm.density(y, display = "image")


#  A three-dimensional example
y <- cbind(rnorm(50), rnorm(50), rnorm(50))
sm.density(y)

Run the code above in your browser using DataLab