kcde function

Kernel cumulative distribution/survival function estimate

Kernel cumulative distribution/survival function estimate

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

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

Returns

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 Pr(X<=x)Pr(X<=x) is estimated, otherwise if tail.flag="upper.tail", it is the survival function P(X>x)P(X>x). For d>1d>1, Pr(X<=x)!=1−Pr(X>x)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.

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 packageRead PDF manual