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

1 2 3 4 5 | ```
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", Hfun.pilot="dscalar")
``` |

`x` |
matrix of data values |

`H,hs` |
bandwidth matrix. If these are missing, |

`Hfun` |
bandwidth matrix function. If missing, |

`Hfun.pilot` |
pilot bandwidth matrix - see |

`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. |

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`

.

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
( |

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.

`kcde`

, `kde`

1 2 3 4 5 |

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