Hpi, Hpi.diag {ks} | R Documentation |
Plug-in bandwidth matrix for bivariate data.
Hpi(x, nstage=2, pilot="samse", pre="sphere", Hstart) Hpi.diag(x, nstage=2, pilot="amse", pre="scale", Hstart)
x |
matrix of data values |
nstage |
number of stages in the plug-in bandwidth selector (1 or 2) |
pilot |
"amse" = AMSE-optimal pilot bandwidths,
"samse" = single SAMSE-optimal pilot bandwidth |
pre |
"scale" = pre-scaling, "sphere" = pre-sphering |
Hstart |
initial bandwidth matrix, used in numerical optimisation |
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. Both of these pilot bandwidths require numerical optimisation.
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 matrix.
Wand, M.P. & Jones, M.C. (1994) Multivariate plugin bandwidth selection. Computational Statistics 9, 97-116.
Duong, T. & Hazelton, M.L. (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Journal of Nonparametric Statistics 15, 17-30.
data(unicef) Hpi(unicef, nstage=1, pilot="amse", pre="scale") Hpi(unicef, nstage=2, pilot="samse", pre="sphere") Hpi.diag(unicef, nstage=2, pilot="amse", pre="scale")