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: denci Description: computes pointwise confidence intervals with prespecified confidence level for univariate density estimation. The computation uses WARPing.

Reference(s):
Haerdle (1990): Applied Nonparametric Regression Haerdle (1991): Smoothing Techniques

 Usage: {fh, clo, cup} = denci(x {,h {,alpha {,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). alpha confidence level, If not given, 0.05 is used. K string, kernel function on [-1,1]. 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. clo m x 2 matrix, the first column is a grid and the second column contains the lower confidence bounds for that grid. cup m x 2 matrix, the first column is a grid and the second column contains the upper confidence bounds for that grid.

Example:
```library("smoother")
library("plot")
x = 5*normal(200)+10
{fh, clo, cup} = denci(x,3)
;
plot(fh,clo,cup)

```
Result:
```Pointwise confidence intervals at confidence level
alpha = 0.05 for a normal density from N(10,25)
are pictured using Quartic kernel (default) and
bandwidth h=3.
```

Author: L. Yang, M. Mueller, 19990413
(C) MD*TECH Method and Data Technologies, 05.02.2006