density {base}

R Documentation

Kernel Density Estimation

Description

The function density computes kernel density estimates with the given kernel and bandwidth (which is the standard deviation of the kernel).

The functions bw.ucv, bw.bcv and bw.sj provide automated ways of selecting a bandwith for density estimates (assuming a Gaussian kernel). The techniques used are as follows; bw.ucv uses unbiased cross-validation, bw.bcv uses biased cross-validation and bw.sj uses the technique of Sheather and Jones. These cross-validation techniques are based on code from the Venables and Ripley MASS package.

The generic functions plot and print have methods for density objects.

The algorithm used in density disperses the mass of the empirical distribution function over a regular grid and then uses the fast Fourier transform to convolve this approximation with a discretized version of the kernel.

Usage

density(x, n=512, kernel="gaussian", bw, adjust=1, width,
        from, to, cut=3)

bw.ucv(x, samples=100)
bw.bcv(x, samples=100)
bw.sj(x, samples=100)

print(dobj)
plot(dobj, ...)

Arguments

x	the values for which the estimate is to be computed.
n	the number of equally spaced points at which the density is to be estimated. This is rounded up to the next power of 2, with a minimum value of 512.
kernel	a character string giving the smoothing kernel to be used. This must be one of "gaussian", "rectangular", "triangular", or "cosine", and may be abbrevited to a single letter.
bw	the smoothing bandwith to be used. This is the standard deviation of the smoothing kernel. It defaults to 1.06 times the minimum of the standard deviation and the interquartile range divided by 1.34 times the sample size to the negative one fifth power. The specified value of bw is multiplied by adjust.
adjust	the bandwith used is actually adjust*bw. This makes it easy to specify values like “half the default” bandwidth.
width	this exists for compatibility with S.
from, to	the left and right-most points of the grid at which the density is to be estimated.
cut	by default, the values of left and right are cut bandwiths beyond the extremes of the data.
samples	the sample size to take in the bandwidth selection functions. If samples is non-positive, the entire data set is used.
dobj	a “density” object.
...	plotting parameters.

Value

An object with class “density”. The underlying structure is a list containing the following components.

x	the coordinates of the points where the density is estimated.
y	the estimated density values.
bw	the bandwidth used.
n	the sample size length(x).
call	the call which produced the result.
data.name	the deparsed name of the x argument.

References

Silverman, B. W. (1986). Density Estimation. London: Chapman and Hall.

Venables, W. N. and B. D. Ripley (1994). Modern Applied Statistics with S-Plus. New York: Springer.

Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.

Sheather, S. J. and M. C. Jones (1991). “A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. B, 683-690.

See Also

convolve, hist.

Examples

# The Old Faithful geyser data
data(faithful)
d <- density(faithful$eruptions, bw=0.15)
d
plot(d)

plot(d, type="n")
polygon(d, col="wheat")

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