kcde: Kernel cumulative distribution/survival function estimate

In ks: Kernel Smoothing

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", pre=TRUE)
Hpi.diag.kcde(x, nstage=2, pilot, Hstart, binned, bgridsize, amise=FALSE,
  verbose=FALSE, optim.fun="optim", pre=TRUE)
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
pre	flag for pre-scaling data. Default is TRUE.
object	object of class kcde
...	other parameters

Details

If tail.flag="lower.tail" then the cumulative distribution function \mathrm{Pr}(\bold{X}\leq\bold{x}) is estimated, otherwise if tail.flag="upper.tail", it is the survival function \mathrm{Pr}(\bold{X}>\bold{x}). For d>1, \mathrm{Pr}(\bold{X}\leq\bold{x}) \neq 1 - \mathrm{Pr}(\bold{X}>\bold{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.

See Also

kde, plot.kcde

Examples

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

## See other examples in ? plot.kcde

ks documentation built on Sept. 30, 2024, 9:15 a.m.