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

```
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=TRUE,
approx.cont=TRUE, boundary.supp, marginal="kernel", Hfun.pilot="dscalar")
```

x

matrix of data values

H,hs

bandwidth matrix. If these are missing, `Hpi.kcde`

or
`hpi.kcde`

or `hpi`

is called by default.

Hfun

bandwidth matrix function. If missing, `Hpi`

is the
default. This is called only when `H`

is missing.

Hfun.pilot

pilot bandwidth matrix - see `Hpi`

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. 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 TRUE.

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.

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

pseudo-uniform data points

data points - same as input

marginal function used to compute pseudo-uniform data

flag for data points in the boundary region
(`kcopula.de`

only)

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. 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`

.

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.

```
# NOT RUN {
library(MASS)
data(fgl)
x <- fgl[,c("RI", "Na")]
Chat <- kcopula(x=x)
plot(Chat, disp="persp", thin=3, col="white", border=1)
# }
```

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