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
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.
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. 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.
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)
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.