H.inv.select {snfa}

Bandwidth matrix selection

Description

Computes inverse of bandwidth matrix using rule-of-thumb from Silverman (1986).

Usage

H.inv.select(X, H.mult = 1)

Arguments

X

Matrix of inputs

H.mult

Scaling factor for rule-of-thumb smoothing matrix

Details

This method performs selection of (inverse) multivariate bandwidth matrices using Silverman's (1986) rule-of-thumb. Specifically, Silverman recommends setting the bandwidth matrix to

H_{jj}^{1/2} = \left(\frac{4}{M + 2}\right)^{1 / (M + 4)}\times N^{-1 / (M + 4)}\times \mbox{sd}(x^j) \mbox{\ \ \ \ for }j=1,...,M

H_{ab} = 0\mbox{\ \ \ \ for }a\neq b

where M is the number of inputs, N is the number of observations, and \mbox{sd}(x^j) is the sample standard deviation of input j.

Value

Returns inverse bandwidth matrix

References

Silverman BW (1986). Density estimation for statistics and data analysis, volume 26. CRC press.

Examples

data(USMacro)

USMacro <- USMacro[complete.cases(USMacro),]

#Extract data
X <- as.matrix(USMacro[,c("K", "L")])

#Generate bandwidth matrix
print(H.inv.select(X))
#              [,1]         [,2]
# [1,] 3.642704e-08 0.000000e+00
# [2,] 0.000000e+00 1.215789e-08