Normal scale bandwidth

Description

Normal scale bandwidth.

Usage

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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

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.

Value

Full normal scale bandwidth matrix.

References

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

Examples

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library(MASS)
data(forbes)
Hns(forbes, deriv.order=2)
hns(forbes$bp, deriv.order=2)

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