Hpi, Hpi.diag, hpi {ks} | R Documentation |
Plug-in bandwidth for for 1- to 6-dimensional data.
Hpi(x, nstage=2, pilot="samse", pre="sphere", Hstart, binned=FALSE, bgridsize, amise=FALSE) Hpi.diag(x, nstage=2, pilot="amse", pre="scale", Hstart, binned=FALSE, bgridsize) hpi(x, nstage=2, binned=TRUE, bgridsize)
x |
vector or matrix of data values |
nstage |
number of stages in the plug-in bandwidth selector (1 or 2) |
pilot |
"amse" = AMSE pilot bandwidths,
"samse" = single SAMSE pilot bandwidth,
"unconstr" = unconstrained pilot bandwidth matrix |
pre |
"scale" = pre-scaling, "sphere" = pre-sphering |
Hstart |
initial bandwidth matrix, used in numerical optimisation |
binned |
flag for binned kernel estimation |
bgridsize |
vector of binning grid sizes - required only if binned=TRUE |
amise |
flag for returning estimated AMISE |
hpi
is the univariate plug-in
selector of Sheather & Jones (1991). Hpi
is a
multivariate generalisation of this.
Use Hpi
for full bandwidth matrices and Hpi.diag
for diagonal bandwidth matrices.
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 pilot bandwidths are
available for d = 1, ..., 5 (but are extremely computationally
intensive for the latter dimensions). See Chac'on & Duong (2008).
For d = 1, the selector hpi
is exactly the same as
KernSmooth's dpik
. This is always computed as binned
estimator. For d = 2, 3, 4 and binned=TRUE
,
estimates are computed over a binning grid defined
by bgridsize
. Otherwise it's computed exactly.
For details on the pre-transformations in pre
, see
pre.sphere
and pre.scale
.
If Hstart
is not given then it defaults to
k*var(x)
where k =
4/(n*(d + 2))^(2/(d+
4)), n = sample size, d = dimension of data.
Plug-in bandwidth. If amise=TRUE
then the plug-in
bandwidth plus the estimated AMISE is returned in a list.
Chac'on, J.E. & Duong, T. (2008) Multivariate plug-in bandwidth selection with unconstrained pilot matrices. Submitted.
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 estimatio. 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.
data(unicef) Hpi(unicef) Hpi(unicef, pilot="unconstr") Hpi.diag(unicef, binned=TRUE) hpi(unicef[,1])