ks (version 1.9.5)

Hns: Normal scale bandwidth

Description

Normal scale bandwidth.

Usage

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

Arguments

x

vector/matrix of data values

deriv.order

derivative order

Value

• Full normal scale bandwidth matrix.

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

x <- rmvnorm.mixt(1000)
Hns(x, deriv.order=1)
hns(x[,1], deriv.order=1)