kernelboot: bw.silv – R documentation

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kernelboot

bw.silv

Bandwidth selector for multivariate kernel density estimation

Description

Rule of thumb bandwidth selectors for Gaussian kernels as described by Scott (1992) and Silverman (1986).

Usage

bw.silv(x, na.rm = FALSE)

bw.scott(x, na.rm = FALSE)

Arguments

`x`	numeric matrix or data.frame.
`na.rm`	a logical value indicating whether `NA` values should be stripped before the computation proceeds.

Details

Scott's (1992) rule is defined as

H = n^(-2/(m+4)) * S

Silverman's (1986; see Chacon, Duong and Wand, 2011) rule is defined as

H = (4/(n*(m+2)))^(2/(m+4)) * S

where m is number of variables, n is sample size, S is the empirical covariance matrix. The bandwidth is returned as a covariance matrix, so to use it for a product kernel, take square root of it's diagonal: sqrt(diag(H)).

bw.silv corresponds to Hns method with deriv.order=0 from the ks package.

References

Silverman, B.W. (1986). Density estimation for statistics and data analysis. Chapman and Hall/CRC.

Wand, M.P. and Jones, M.C. (1995). Kernel smoothing. Chapman and Hall/CRC.

Scott, D.W. (1992). Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons.

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

Epanechnikov, V.A. (1969). Non-parametric estimation of a multivariate probability density. Theory of Probability & Its Applications, 14(1): 153-158.