hnorm function

Normal optimal choice of smoothing parameter in density estimation

This functions evaluates the smoothing parameter which is asymptotically optimal for estimating a density function when the underlying distribution is Normal. Data in one, two or three dimensions can be handled.

hnorm(x, weights)

Arguments

• x: a vector, or matrix with two or three columns, containing the data.
• weights: an optional vector of integer values which allows the kernel functions over the observations to take different weights when they are averaged to produce a density estimate. This is useful, in particular, for censored data and to construct an estimate from binned data.

Returns

the value of the asymptotically optimal smoothing parameter for Normal case.

Details

See Section 2.4.2 of the reference below.

Note

As from version 2.1 of the package, a similar effect can be obtained with the new function h.select, via h.select(x, method="normal", weights=weights) or simply h.select(x). Users are encouraged to adopt this route, since hnorm might be not accessible directly in future releases of the package.

References

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis:

the Kernel Approach with S-Plus Illustrations.

Oxford University Press, Oxford.

See Also

h.select, hcv, hsj

Examples

x <- rnorm(50)
hnorm(x)