Hscv: Smoothed cross-validation (SCV) bandwidth matrix selector
for bivariate data
Description
SCV bandwidth matrix for 2- to 6-dimensional data.
Usage
Hscv(x, pre="sphere", Hstart)
Arguments
x
matrix of data values
pre
"scale" = pre-scaling, "sphere" = pre-sphering
Hstart
initial bandwidth matrix, used in numerical
optimisation
Value
Full SCV bandwidth matrix. Please note that a diagonal version of this
selector is not available.
Details
This SCV selector is a generalisation of the univariate SCV
selector of Jones, Marron & Park (1991).
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.
References
Jones, M.C., Marron, J.~S. & Park, B.U. (1991) A simple root n
bandwidth selector. The Annals of Statistics19, 1919--1932.
Duong, T. & Hazelton, M.L. (2004) Cross-validation bandwidth
matrices for multivariate kernel density estimation. Scandinavian Journal
of Statistics. In press.