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kcde

Kernel cumulative distribution/survival function estimate

Description

Kernel cumulative distribution/survival function estimate for 1- to 3-dimensional data.

Usage

kcde(x, H, h, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points,
  binned, bgridsize, positive=FALSE, adj.positive, w, verbose=FALSE,
  tail.flag="lower.tail")
Hpi.kcde(x, nstage=2, pilot, Hstart, binned, bgridsize, amise=FALSE,
  verbose=FALSE, optim.fun="optim")
Hpi.diag.kcde(x, nstage=2, pilot, Hstart, binned, bgridsize, amise=FALSE,
  verbose=FALSE, optim.fun="optim")
hpi.kcde(x, nstage=2, binned, amise=FALSE)

## S3 method for class 'kcde'
predict(object, ..., x)

Arguments

`x`	matrix of data values
`H,h`	bandwidth matrix/scalar bandwidth. If these are missing, then `Hpi.kcde` or `hpi.kcde` 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`	vector or matrix of points at which estimate is evaluated
`binned`	flag for binned estimation. Default is FALSE.
`bgridsize`	vector of binning grid sizes
`positive`	flag if 1-d data are positive. Default is FALSE.
`adj.positive`	adjustment applied to positive 1-d data
`w`	not yet implemented
`verbose`	flag to print out progress information. Default is FALSE.
`tail.flag`	"lower.tail" = cumulative distribution, "upper.tail" = survival function
`nstage`	number of stages in the plug-in bandwidth selector (1 or 2)
`pilot`	"dscalar" = single pilot bandwidth (default for `Hpi.diag.kcde` "dunconstr" = single unconstrained pilot bandwidth (default for `Hpi.kcde`
`Hstart`	initial bandwidth matrix, used in numerical optimisation
`amise`	flag to return the minimal scaled PI value
`optim.fun`	optimiser function: one of `nlm` or `optim`
`object`	object of class `kcde`
`...`	other parameters

Details

If tail.flag="lower.tail" then the cumulative distribution function Pr(X<=x) is estimated, otherwise if tail.flag="upper.tail", it is the survival function P(X>x). For d>1, Pr(X<=x) != 1-Pr(X>x).

If the bandwidth H is missing in kcde, then the default bandwidth is the plug-in selector Hpi.kcde. Likewise for missing h. No pre-scaling/pre-sphering is used since the Hpi.kcde is not invariant to translation/dilation.

The effective support, binning, grid size, grid range, positive, optimisation function parameters are the same as kde.

Value

A kernel cumulative distribution estimate is an object of class kcde which is a list with fields:

`x`	data points - same as input
`eval.points`	vector or list of points at which the estimate is evaluated
`estimate`	cumulative distribution/survival function estimate at `eval.points`
`h`	scalar bandwidth (1-d only)
`H`	bandwidth matrix
`gridtype`	"linear"
`gridded`	flag for estimation on a grid
`binned`	flag for binned estimation
`names`	variable names
`w`	vector of weights
`tail`	"lower.tail"=cumulative distribution, "upper.tail"=survival function

References

Duong, T. (2016) Non-parametric smoothed estimation of multivariate cumulative distribution and survival functions, and receiver operating characteristic curves. Journal of the Korean Statistical Society, 45, 33-50.

Examples

library(MASS)
data(iris)
Fhat <- kcde(iris[,1:2])  
predict(Fhat, x=as.matrix(iris[,1:2]))

## See other examples in ? plot.kcde

ks

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06