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

 Library: smoother See also: denxest denxcb denest denci dencb

 Quantlet: denxci Description: computes pointwise confidence intervals with prespecified confidence level for univariate density estimation.

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

 Usage: {fh, clo, cup} = denxci(x {,h {,alpha {,K} {,xv}}}) 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. xv m x 1, values of the independent variable on which to compute the density estimate. If not given, x is used. Output: fh n x 2 or m x 2 matrix, the first column is the sorted first column of x or the sorted xv, the second column contains the density estimate on on the values of the first column. clo n x 2 or m x 2 matrix, the first column is the sorted first column of x or the sorted xv, the second column contains the lower confidence bounds on the values of the first column. cup n x 2 or m x 2 matrix, the first column is the sorted first column of x or the sorted xv, the second column contains the upper confidence bounds on the values of the first column.

Note:
This function does an exact computation, i.e. requires O(n^2) operations for estimating the regression function on all observations. For exploratory purposes, the macro "denci" is recommended, which uses the faster WARPing method.

Example:
```library("smoother")
library("plot")
x = 5*normal(200)+10
{fh, clo, cup} = denxci(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: Marlene Mueller 990413
(C) MD*TECH Method and Data Technologies, 05.02.2006