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: denest denci denxest denxci denxcb

Quantlet: dencb
Description: computes uniform confidence bands with prespecified confidence level for univariate density estimation.

Reference(s):

Usage: {fh, clo, cup} = dencb(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] with K(-1)=K(1)=0. 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} = dencb(x,3)
;
fh=setmask(fh,"line","blue")
clo=setmask(clo,"line","blue","thin","dashed")
cup=setmask(cup,"line","blue","thin","dashed")
plot(fh,clo,cup)

Result:
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 990413
(C) MD*TECH Method and Data Technologies, 05.02.2006