Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: Rdenbest Description: evaluates a kernel estimate of an integrated squared density (derivative) using the normal kernel for a (vector of) bandwidth(s) h. This quantlet is a variation of Rdenxest and uses linearly prebinned data for faster computation.

Reference(s):
Wand, M. P. and Jones, M. C. (1995). Kernel smoothing. Chapman and Hall. London.

 Usage: Rh = Rdenbest(der, nx, binw, d, h, diag) Input: der scalar, order of derivative der = 0,1,2,... nx scalar, number of data points binw m x 1 vector of bin weights = autocovariance of the bin counts d Defintion scalar, binwidth p x 1 vector of bandwidths h scalar; if set to 0, the diagonal terms are removed from the estimate, otherwise included Output: Rh p x 1 vector of the functional estimates

Example:
```library("smoother")
library("xplore")
randomize(0)
n = 1000
s = 2
diag = 1
h = #(0.1, 0.2, 0.3)
d = 0.01
{w,mu,sigma} = normalmixselect("Marron_Wand_3")
x = normalmix(n, w, mu, sigma)
{bingrid, bincounts} = binlindata(x, d, 0)
binw = binweights(bincounts)
Rh = Rdenbest(s, n, binw, d, h, diag)
h ~ Rh

```
Result:
```computes the kernel estimates for the integrated squared
second density derivative at three different bandwidths
based on a sample of size 1000 generated from a normal
mixture example density using linear binned data:

Contents of _tmp
[1,]      0.1   1020.1
[2,]      0.2   145.35
[3,]      0.3   32.609
```

Author: J.-U. Scheer, 20020406 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006