Kernel functional estimate

Kernel functional estimate for 1- to 6-dimensional data.

Usage

kfe(x, G, deriv.order, inc=1, binned, bin.par, bgridsize, deriv.vec=TRUE,
    add.index=TRUE, verbose=FALSE)
Hpi.kfe(x, nstage=2, pilot, pre="sphere", Hstart, binned=FALSE, 
    bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="optim")
Hpi.diag.kfe(x, nstage=2, pilot, pre="scale", Hstart, binned=FALSE,
    bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="optim")
hpi.kfe(x, nstage=2, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0)

Arguments

x: vector/matrix of data values
nstage: number of stages in the plug-in bandwidth selector (1 or 2)
pilot: "dscalar" = single pilot bandwidth (default)
"dunconstr" = single unconstrained pilot bandwidth
pre: "scale" = pre.scale, "sphere" = pre.sphere
Hstart: initial bandwidth matrix, used in numerical optimisation
binned: flag for binned estimation
bgridsize: vector of binning grid sizes
amise: flag to return the minimal scaled PI value
deriv.order: derivative order
verbose: flag to print out progress information. Default is FALSE.
optim.fun: optimiser function: one of nlm or optim
G: pilot bandwidth matrix
inc: 0=exclude diagonal, 1=include diagonal terms in kfe calculation
bin.par: binning parameters - output from binning
deriv.vec: flag to compute duplicated partial derivatives in the vectorised form. Default is FALSE.
add.index: flag to output derivative indices matrix. Default is true.

Value

Plug-in bandwidth matrix for \(r\)-th order kernel functional estimator.

Details

Hpi.kfe is the optimal plug-in bandwidth for \(r\)-th order kernel functional estimator based on the unconstrained pilot selectors of Chacon & Duong (2010). hpi.kfe is the 1-d equivalent, using the formulas from Wand & Jones (1995, p.70).

kfe does not usually need to be called explicitly by the user.

References

Chacon, J.E. & Duong, T. (2010) Multivariate plug-in bandwidth selection with unconstrained pilot matrices. Test 19, 375–398.