bw.mse.pdf.asym: Find asymptotically optimal bandwidth for KDE by minimizing...
In MRPP: Multiresponse permutation procedure and its variable importance and variable selection methods.

Description Usage Arguments Details Value Author(s) References See Also Examples

Find asymptotically optimal bandwidth for Gaussian kernel density estimation by minimizing mean squared error at the first data point.

1	bw.mse.pdf.asym(x,iter.max=1L,eps=1e-6,start.bw=bw.nrd, verbose=FALSE)

`x`	A numeric vector whose density is to be estimated.
`iter.max`	The max number of iterations. For an iterative procedure, set this to be greater than 1L.
`eps`	A small positive number such that iterations are terminated when the difference between successive bandwidths is below `eps`.
`start.bw`	A function, a character, or a positive number. If being a function or a character, the corresponding function will be called with `x` as the only argument to get the initial bandwidth. When it is a number, it will be used as the starting bandwidth directly.
`verbose`	Logical, when `TRUE`, the bandwidth for each iteration will be printed.

The procedure starts from the starting bandwidth specified by start.bw. The new bandwidth will be computed as

( {Rf(x_1)} / [N{f''(x_1)}^2] )^{1/5}

where R is approximately 0.2821, N is the sample size and f is the density estimate using the current bandwidth.

A numeric positive scalar, giving the final bandwidth.

Long Qu

Parzen, E. (1962). On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics 33: 1065–1076.

Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley, New York.

Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.

density, kdde

set.seed(23490)
x=rnorm(100)
bw.mse.pdf.asym(x)
## Not run: 
plot(density(x, bw.mse.pdf.asym(x)), ylim=c(0,dnorm(0)))
abline(v=x[1L])
curve(dnorm, lty=3, col='grey', add=TRUE)

## End(Not run)