Plug-in bandwidth for for 1- to 6-dimensional data.
Hpi(x, nstage=2, pilot, pre="sphere", Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm") Hpi.diag(x, nstage=2, pilot, pre="scale", Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, verbose=FALSE, optim.fun="nlm") hpi(x, nstage=2, binned=TRUE, bgridsize, deriv.order=0)
vector or matrix of data values
number of stages in the plug-in bandwidth selector (1 or 2)
"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 PI value
flag to print out progress information. Default is FALSE.
optimiser function: one of
amise=TRUE then the minimal scaled PI value is returned too.
hpi(,deriv.order=0) is the univariate plug-in
selector of Wand & Jones (1994), i.e. it is exactly the same as
dpik. For deriv.order>0, the formula is
taken from Wand & Jones (1995).
Hpi is a multivariate
generalisation of this. Use
Hpi for unconstrained bandwidth matrices and
Hpi.diag for diagonal bandwidth matrices.
The default pilot is
"samse" for d=2,r=0, and
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
estimates are computed over a binning grid defined
bgridsize. Otherwise it's computed exactly.
Hstart is not given then it defaults to
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.
Wand, M.P. & Jones, M.C. (1994) Multivariate plugin bandwidth selection. Computational Statistics. 9, 97-116.