Skip to contents

Normal scale bandwidth

Hns.Rd

Normal scale bandwidth.

Usage

Hns(x, deriv.order=0)
Hns.diag(x)
hns(x, deriv.order=0)
Hns.kcde(x)
hns.kcde(x)

Arguments

x

vector/matrix of data values

deriv.order

derivative order

Value

Normal scale bandwidth.

Details

Hns is equal to (4/(n*(d+2*r+2)))^(2/(d+2*r+4))*var(x), n = sample size, d = dimension of data, r = derivative order. hns is the analogue of Hns for 1-d data. These can be used for density (derivative) estimators kde, kdde. The equivalents for distribution estimators kcde are Hns.kcde and hns.cde.

References

Chacon J.E., Duong, T. & Wand, M.P. (2011) Asymptotics for general multivariate kernel density derivative estimators. Statistica Sinica 21, 807–840.

Examples

data(forbes, package="MASS")
Hns(forbes, deriv.order=2)
#>             bp     pres
#> bp   16.387047 8.568663
#> pres  8.568663 4.505593
hns(forbes$bp, deriv.order=2)
#> [1] 3.950731