Hscv function

Smoothed cross-validation (SCV) bandwidth selector

Smoothed cross-validation (SCV) bandwidth selector

SCV bandwidth for 1- to 6-dimensional data.

Hscv(x, nstage=2, pre="sphere", pilot, Hstart, binned, 
     bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="optim")
Hscv.diag(x, nstage=2, pre="scale", pilot, Hstart, binned, 
     bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="optim")
hscv(x, nstage=2, binned=TRUE, bgridsize, plot=FALSE)

Arguments

  • x: vector or matrix of data values

  • pre: "scale" = pre.scale, "sphere" = pre.sphere

  • pilot: "amse" = AMSE pilot bandwidths

    "samse" = single SAMSE pilot bandwidth

    "unconstr" = single unconstrained pilot bandwidth

    "dscalar" = single pilot bandwidth for deriv.order>0

    "dunconstr" = single unconstrained pilot bandwidth for deriv.order>0

  • Hstart: initial bandwidth matrix, used in numerical optimisation

  • binned: flag for binned kernel estimation

  • bgridsize: vector of binning grid sizes

  • amise: flag to return the minimal scaled SCV value. Default is FALSE.

  • deriv.order: derivative order

  • verbose: flag to print out progress information. Default is FALSE.

  • optim.fun: optimiser function: one of nlm or optim

  • nstage: number of stages in the SCV bandwidth selector (1 or 2)

  • plot: flag to display plot of SCV(h) vs h (1-d only). Default is FALSE.

Returns

SCV bandwidth. If amise=TRUE then the minimal scaled SCV value is returned too.

Details

hscv is the univariate SCV selector of Jones, Marron & Park (1991). Hscv is a multivariate generalisation of this, see Duong & Hazelton (2005). Use Hscv for unconstrained bandwidth matrices and Hscv.diag

for diagonal bandwidth matrices.

The default pilot is "samse" for d=2, r=0, and "dscalar" otherwise. For SAMSE pilot bandwidths, see Duong & Hazelton (2005). Unconstrained and higher order derivative pilot bandwidths are from Chacon & Duong (2011).

For d=1, the selector hscv is not always stable for large sample sizes with binning. Examine the plot from hscv(, plot=TRUE) to determine the appropriate smoothness of the SCV function. Any non-smoothness is due to the discretised nature of binned estimation.

For details about the advanced options for binned, Hstart, optim.fun, see Hpi.

References

Chacon, J.E. & Duong, T. (2011) Unconstrained pilot selectors for smoothed cross validation. Australian & New Zealand Journal of Statistics, 53 , 331-351.

Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics, 32 , 485-506.

Jones, M.C., Marron, J.S. & Park, B.U. (1991) A simple root nn

bandwidth selector. Annals of Statistics, 19 , 1919-1932.

See Also

Hbcv, Hlscv, Hpi

Examples

data(unicef)
Hscv(unicef)
hscv(unicef[,1])
ks packageRead PDF manual