Kernel cumulative distribution/survival function estimate

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

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

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.

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

data(iris)
Fhat <- kcde(iris[,1:2])  
predict(Fhat, x=as.matrix(iris[,1:2]))
#>   [1] 0.183688941 0.053679294 0.059165038 0.037235867 0.171233241 0.331399053
#>   [7] 0.060723956 0.141833006 0.010850701 0.070540280 0.306228130 0.098589783
#>  [13] 0.044178204 0.011025553 0.484519776 0.464239041 0.331399053 0.183688941
#>  [19] 0.423281009 0.220986454 0.234375209 0.212289270 0.069457262 0.142469530
#>  [25] 0.098589783 0.064059122 0.141833006 0.209474854 0.186747475 0.059165038
#>  [31] 0.058529954 0.234375209 0.268880526 0.383218639 0.070540280 0.103638300
#>  [37] 0.290469242 0.143038196 0.015594786 0.164143253 0.158039099 0.003237532
#>  [43] 0.025577055 0.158039099 0.220986454 0.044178204 0.220986454 0.046362995
#>  [49] 0.274858173 0.123436960 0.590942414 0.464724980 0.506168207 0.023924663
#>  [55] 0.246962280 0.125228142 0.480562519 0.014070811 0.321952279 0.046141146
#>  [61] 0.002612815 0.233676715 0.022085413 0.237964280 0.131923170 0.476631014
#>  [67] 0.159986140 0.115444809 0.025314094 0.055813718 0.310599008 0.193531790
#>  [73] 0.097528227 0.193531790 0.294078825 0.391202688 0.268629462 0.405853834
#>  [79] 0.216850377 0.081671601 0.036006132 0.036006132 0.115444809 0.141262255
#>  [85] 0.119389914 0.418306942 0.476631014 0.044375268 0.159986140 0.049507527
#>  [91] 0.063142109 0.284730436 0.091107545 0.012207127 0.089343058 0.183378215
#>  [97] 0.152213679 0.258116833 0.026984633 0.125228142 0.480562519 0.115444809
#> [103] 0.442309263 0.276988979 0.374050503 0.465441626 0.017870367 0.364037178
#> [109] 0.109980288 0.822232406 0.492401678 0.183971408 0.417938760 0.062210492
#> [115] 0.142514569 0.464724980 0.374050503 0.917741051 0.161192058 0.022085413
#> [121] 0.576946795 0.108544065 0.290742107 0.175008490 0.596886547 0.612234147
#> [127] 0.209055514 0.284730436 0.236033529 0.447845419 0.284907984 0.927586071
#> [133] 0.236033529 0.223357182 0.117962727 0.468980309 0.523170273 0.412203734
#> [139] 0.259355951 0.506168207 0.476631014 0.506168207 0.115444809 0.560136651
#> [145] 0.596886547 0.405853834 0.097528227 0.374050503 0.488340514 0.233676715

## See other examples in ? plot.kcde