Hpi(x, nstage=2, pilot="samse", pre="sphere", Hstart,
binned=FALSE, bgridsize, amise=FALSE, kfold=1)
Hpi.diag(x, nstage=2, pilot="amse", pre="scale", Hstart,
binned=FALSE, bgridsize, kfold=1)
hpi(x, nstage=2, binned=TRUE, bgridsize)"amse" = AMSE pilot bandwidths,
"samse" = single SAMSE pilot bandwidth,
"unconstr" = unconstrained pilot bandwidth matrix"scale" = pre-scaling, "sphere" = pre-spheringamise=TRUE then the plug-in
bandwidth plus the estimated AMISE is returned in a list.hpi is the univariate plug-in
selector of Wand & Jones (1994). 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
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 =
$\left[\frac{4}{n(d+2)}\right]^{2/(d+4)}$, n = sample size, d = dimension of data.
For large samples, k-fold bandwidth selection can significantly reduce computation time. The full
data sample is partitioned into k sub-samples and a bandwidth matrix is computed for each of these
sub-samples. The bandwidths are averaged and re-weighted to serve as a proxy for the full sample selector.
data(unicef)
Hpi(unicef)
Hpi(unicef, pilot="unconstr")
Hpi.diag(unicef, binned=TRUE)
hpi(unicef[,1])Run the code above in your browser using DataLab