# 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

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

## Usage

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

## Arguments

 `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.

## Details

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.

## Value

A numeric positive scalar, giving the final bandwidth.

Long Qu

## References

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`
 ```1 2 3 4 5 6 7 8 9``` ```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) ```