kde.boundary: Kernel density estimate for bounded data

In ks: Kernel Smoothing

Kernel density estimate for bounded data

Description

Kernel density estimate for bounded 1- to 3-dimensional data.

Usage

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

Arguments

x	matrix of data values
H, h	bandwidth matrix/scalar bandwidth. If these are missing, Hpi or hpi is called by default.
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.
boundary.supp	effective support for boundary region
boundary.kernel	"beta" = beta boundary kernel, "linear" = linear boundary kernel
verbose	flag to print out progress information. Default is FALSE.

Details

There are two forms of density estimates which are suitable for bounded data, based on the modifying the kernel function. For boundary.kernel="beta", the 2nd form of the Beta boundary kernel of Chen (1999) is employed. It is suited for rectangular data boundaries.

For boundary.kernel="linear", the linear boundary kernel of Hazelton & Marshall (2009) is employed. It is suited for arbitrarily shaped data boundaries, though it is currently only implemented for rectangular boundaries.

Value

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

References

Chen, S. X. (1999) Beta kernel estimators for density functions. Computational Statistics and Data Analysis, 31, 131–145.

Hazelton, M. L. & Marshall, J. C. (2009) Linear boundary kernels for bivariate density estimation. Statistics and Probability Letters 79, 999–1003.

See Also

kde

Examples

data(worldbank)
wb <- as.matrix(na.omit(worldbank[,c("internet", "ag.value")]))
fhat <- kde(x=wb)
fhat.beta <- kde.boundary(x=wb, xmin=c(0,0), xmax=c(100,100), boundary.kernel="beta")  
plot(fhat, col=1, xlim=c(0,100), ylim=c(0,100))
plot(fhat.beta, add=TRUE, col=2)
rect(0,0,100,100, lty=2)

fhat.LB <- kde.boundary(x=wb, xmin=c(0,0), xmax=c(100,100), boundary.kernel="linear")
plot(fhat, col=1, xlim=c(0,100), ylim=c(0,100))
plot(fhat.LB, add=TRUE, col=3)
rect(0,0,100,100, lty=2)

ks documentation built on Aug. 4, 2026, 5:07 p.m.