Least-squares cross-validation (LSCV) bandwidth matrix selector for multivariate data

Description

LSCV bandwidth for 1- to 6-dimensional data

Usage

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Hlscv(x, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, 
      verbose=FALSE, optim.fun="nlm", trunc)
Hlscv.diag(x, Hstart, binned=FALSE, bgridsize, amise=FALSE, deriv.order=0, 
      verbose=FALSE, optim.fun="nlm", trunc)
hlscv(x, binned=TRUE, bgridsize, amise=FALSE, deriv.order=0)
Hucv(...)
Hucv.diag(...)
hucv(...)

Arguments

x

vector or matrix of data values

Hstart

initial bandwidth matrix, used in numerical optimisation

binned

flag for binned kernel estimation. Default is FALSE.

bgridsize

vector of binning grid sizes

amise

flag to return the minimal LSCV value. Default is FALSE.

deriv.order

derivative order

verbose

flag to print out progress information. Default is FALSE.

optim.fun

optimiser function: one of nlm or optim

trunc

parameter to control truncation for numerical optimisation. Default is 4 for density.deriv>0, otherwise no truncation. For details see below.

...

parameters as above

Details

hlscv is the univariate LSCV selector of Bowman (1984) and Rudemo (1982). Hlscv is a multivariate generalisation of this. Use Hlscv for full bandwidth matrices and Hlscv.diag for diagonal bandwidth matrices. Hucv, Hucv.diag and hucv are aliases with UCV unbiased cross validation instead of LSCV.

Truncation of the parameter space is usually required for the LSCV selector, for r > 0, to find a reasonable solution to the numerical optimisation. If a candidate matrix H is such that det(H) is not in [1/trunc, trunc]*det(H0) or abs(LSCV(H)) > trunc*abs(LSCV0) then the LSCV(H) is reset to LSCV0 where H0=Hns(x) and LSCV0=LSCV(H0).

For details about the advanced options for binned,Hstart, see Hpi.

Value

LSCV bandwidth. If amise=TRUE then the minimal LSCV value is returned too.

References

Bowman, A. (1984) An alternative method of cross-validation for the smoothing of kernel density estimates. Biometrika. 71, 353-360.

Rudemo, M. (1982) Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics. 9, 65-78.

See Also

Hbcv, Hpi, Hscv

Examples

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library(MASS)
data(forbes)
Hlscv(forbes)
hlscv(forbes$bp)

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