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: denest Description: estimates a univariate density by kernel density estimation. The computation uses WARPing.

 Usage: fh = denest(x {,h {,K} {,d} }) Input: x n x 1 vector, the data. h scalar, bandwidth. If not given, the rule of thumb bandwidth computed by denrot is used (Silverman's rule of thumb). K string, kernel function on [-1,1] or Gaussian kernel "gau". If not given, the Quartic kernel "qua" is used. d scalar, discretization binwidth. d must be smaller than h. If not given, the minimum of h/3 and (max(x)-min(x))/100 is used. Output: fh m x 2 matrix, the first column is a grid and the second column contains the density estimate on that grid.

Example:
```library("smoother")
library("plot")
;
mu = 10
si = 5
x  = si*normal(200)+mu          ; generate data
;
fh = denest(x)                  ; estimate density
f  = sort(x~pdfn((x-mu)/si)/si) ; true density                   ;             ;
plot(f,fh)                      ; graph functions

```
Result:
```The density estimate (blue) for a normal distribution
with mean mu=10, standard deviation si=5 is pictured
using Quartic kernel (default) and Silverman's
rule-of-thumb bandwidth (default), together with
the true density (thin black).
```
Example:
```library("smoother")
library("plot")
;
mu = 10
si = 5
x  = si*normal(200)+mu           ; generate data
;
fhe= denest(x,3,"epa")           ; estimate density
fhu= denest(x,3,"uni")           ; estimate density
f  = sort(x~pdfn((x-mu)/si)/si)  ; true density
;
plot(f,fhu,fhe)                  ; graph functions

```
Result:
```The density estimate using the Epanechnikov kernel
(green) is compared to the density estimate using
the Uniform kernel (red) and the true density (thin
black). In both cases, bandwidth h=3 is used.
```

Author: W. Haerdle, S. Klinke, L. Yang, M. Mueller, 990413 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006