Kernel copula (density) estimate

Kernel copula and copula density estimator for 2-dimensional data.

Usage

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

Arguments

x: matrix of data values
H,hs: bandwidth matrix. If these are missing, Hpi.kcde/Hpi or hpi.kcde/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: 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.
marginal: "kernel" = kernel cdf or "empirical" = empirical cdf to calculate pseudo-uniform values. Default is "kernel".
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.

Value

A kernel copula estimate, output from kcopula, is an object of class kcopula. A kernel copula density estimate, output from kcopula.de, is an object of class kde. These two classes of objects have the same fields as kcde and kde objects respectively, except for

x: pseudo-uniform data points
x.orig: data points - same as input
marginal: marginal function used to compute pseudo-uniform data
boundary: flag for data points in the boundary region (kcopula.de only)

Details

For kernel copula estimates, a transformation approach is used to account for the boundary effects. If H is missing, the default is Hpi.kcde; if hs are missing, the default is hpi.kcde.

For kernel copula density estimates, for those points which are in the interior region, the usual kernel density estimator (kde) is used. For those points in the boundary region, a product beta kernel based on the boundary corrected univariate beta kernel of Chen (1999) is used (kde.boundary). If H is missing, the default is Hpi.kcde; if hs are missing, the default is hpi.

The effective support, binning, grid size, grid range parameters are the same as for kde.

References

Duong, T. (2014) Optimal data-based smoothing for non-parametric estimation of copula functions and their densities. Submitted.

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

Examples

data(fgl, package="MASS")
x <- fgl[,c("RI", "Na")]
Chat <- kcopula(x=x)
plot(Chat, display="filled.contour", lwd=1)

plot(Chat, display="persp", border=1)