number of stages in the plug-in bandwidth selector (1 or 2)
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
pre
"scale" = pre.scale, "sphere" = pre.sphere
Hstart
initial bandwidth matrix, used in numerical
optimisation
binned
flag for binned kernel estimation. Default is FALSE.
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
Details
hpi(,deriv.order=0) is the univariate plug-in
selector of Wand & Jones (1994), i.e. it is exactly the same as
KernSmooth's dpik. For deriv.order>0, the formula is
taken from Wand & Jones (1995). Hpi is a multivariate
generalisation of this. Use Hpi for full bandwidth matrices and
Hpi.diag for diagonal bandwidth matrices.
The default pilot is "samse" for d=2,r=0, and
"dscalar" otherwise.
For AMSE pilot bandwidths, see Wand & Jones (1994). For
SAMSE pilot bandwidths, see Duong & Hazelton (2003). The latter is a
modification of the former, in order to remove any possible problems
with non-positive definiteness. Unconstrained and higher order
derivative pilot bandwidths are from Chacon & Duong (2010).
For d=1, 2, 3, 4 and binned=TRUE,
estimates are computed over a binning grid defined
by bgridsize. Otherwise it's computed exactly.
If Hstart is not given then it defaults to Hns(x).
Value
Plug-in bandwidth.
If amise=TRUE then the minimal scaled PI value is returned too.
References
Chacon, J.E. & Duong, T. (2010) Multivariate plug-in bandwidth
selection with unconstrained pilot matrices. Test, 19, 375-398.
Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for
bivariate kernel density estimation. Journal of Nonparametric
Statistics. 15, 17-30.
Sheather, S.J. & Jones, M.C. (1991) A reliable data-based bandwidth selection
method for kernel density estimation. Journal of the Royal
Statistical Society Series B. 53, 683-690.