vkde: Variable kernel density estimate.

In ks: Kernel Smoothing

Variable kernel density estimate.

Description

Variable kernel density estimate for 2-dimensional data.

Usage

kde.balloon(x, H, h, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points, 
   binned, bgridsize, w, compute.cont=TRUE, approx.cont=TRUE, verbose=FALSE)
kde.sp(x, H, h, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points, 
   binned, bgridsize, w, compute.cont=TRUE, approx.cont=TRUE, verbose=FALSE)

Arguments

x	matrix of data values
H	bandwidth matrix. If this missing, Hns is called by default.
h	not yet implemented
gridsize	vector of number of grid points
gridtype	not yet implemented
xmin,xmax	vector of minimum/maximum values for grid
supp	effective support for standard normal
eval.points	vector or matrix of points at which estimate is evaluated
binned	flag for binned estimation.
bgridsize	vector of binning grid sizes
w	vector of weights. Default is a vector of all ones.
compute.cont	flag for computing 1% to 99% probability contour levels. Default is TRUE.
approx.cont	flag for computing approximate probability contour levels. Default is TRUE.
verbose	flag to print out progress information. Default is FALSE.

Details

The balloon density estimate kde.balloon employs bandwidths which vary at each estimation point (Loftsgaarden & Quesenberry, 1965). There are as many bandwidths as there are estimation grid points. The default bandwidth is Hns(,deriv.order=2) and the subsequent bandwidths are derived via a minimal MSE formula.

The sample point density estimate kde.sp employs bandwidths which vary for each data point (Abramson, 1982). There are as many bandwidths as there are data points. The default bandwidth is Hns(,deriv.order=4) and the subsequent bandwidths are derived via the Abramson formula.

Value

A variable kernel density estimate for bounded data is an object of class kde.

References

Abramson, I. S. (1982) On bandwidth variation in kernel estimates - a square root law. Annals of Statistics, 10, 1217-1223.

Loftsgaarden, D. O. & Quesenberry, C. P. (1965) A nonparametric estimate of a multivariate density function. Annals of Mathematical Statistics, 36, 1049-1051.

See Also

kde, plot.kde

Examples

data(worldbank)
wb <- as.matrix(na.omit(worldbank[,4:5]))
xmin <- c(-70,-35); xmax <- c(35,70)
fhat <- kde(x=wb, xmin=xmin, xmax=xmax)
fhat.sp <- kde.sp(x=wb, xmin=xmin, xmax=xmax)
zmax <- max(fhat.sp$estimate)
plot(fhat, display="persp", box=TRUE, phi=20, thin=1, border=grey(0,0.2), zlim=c(0,zmax))
plot(fhat.sp, display="persp", box=TRUE, phi=20, thin=1, border=grey(0,0.2), zlim=c(0,zmax))
## Not run: 
fhat.ball <- kde.balloon(x=wb, xmin=xmin, xmax=xmax)
plot(fhat.ball, display="persp", box=TRUE, phi=20, zlim=c(0,zmax))
## End(Not run)

ks documentation built on Aug. 11, 2023, 1:10 a.m.