ks (version 1.8.13)

kcopula: Kernel copula/copula density estimate

Description

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

Arguments

x

matrix of data values

H,hs

bandwidth matrix. If these are missing, Hpi or hpi is called by default.

Hfun

bandwidth matrix function. If missing, Hpi is the default. This is called only when H is missing.

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

points at which estimate is evaluated

binned

flag for binned estimation. Default is FALSE.

bgridsize

vector of binning grid sizes

w

vector of weights. Default is a vector of all ones.

verbose

flag to print out progress information. Default is FALSE.

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 FALSE.

approx.cont

flag for computing approximate probability contour levels. Default is TRUE.

boundary.supp

scaled boundary region is [0, boundary.supp*h] or [1-boundary.supp*h,1] on [0,1]. Default is 1.

Value

• A kernel copula estimate, output from kcopula, is an object of class kcde. A kernel copula density estimate, output from kcopula.de, is an object of class kde.

Details

For kernel copula estimates, a transformation approach is used to account for the boundary effects. For kernel copula density estimates, for those points which are in the interior region, the usual normal 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.

References

Duong, T. (2013) 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.

See Also

kcde, kde

Examples

library(MASS)
data(crabs)
Chat <- kcopula(x=crabs[crabs$sp=="B",4:5])
plot(Chat, disp="persp", thin=3, col="white", border=1)
chat <- kcopula.de(x=crabs[crabs$sp=="B",4:5])
plot(chat, disp="persp", thin=3, theta=40, phi=30, col="white", border=1)