SCV bandwidth for 1- to 6-dimensional data.
Hscv(x, nstage=2, pre="sphere", pilot, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm") Hscv.diag(x, nstage=2, pre="scale", pilot, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm") hscv(x, nstage=2, binned=TRUE, bgridsize, plot=FALSE)
vector or matrix of data values
"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
initial bandwidth matrix, used in numerical optimisation
flag for binned kernel estimation. Default is FALSE.
vector of binning grid sizes
flag to return the minimal scaled SCV value. Default is FALSE.
flag to print out progress information. Default is FALSE.
optimiser function: one of
number of stages in the SCV bandwidth selector (1 or 2)
flag to display plot of SCV(h) vs h (1-d only). Default is FALSE.
SCV bandwidth. If
amise=TRUE then the minimal scaled SCV value is returned too.
hscv is the univariate SCV
selector of Jones, Marron & Park (1991).
Hscv is a
multivariate generalisation of this, see Duong & Hazelton (2005).
Hscv for unconstrained bandwidth matrices and
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
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 n bandwidth selector. Annals of Statistics. 19, 1919-1932.