kde.boundary function

Kernel density estimate for bounded data

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

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.

Returns

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

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.

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")  
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.beta, add=TRUE, col=2)
rect(0,0,100,100, lty=2)
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)