XploRe Help : regxcb

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:	regxest regxci regest regci regcb

Quantlet:		regxcb
Description:		computes uniform confidence bands with a pre-specified confidence level for univariate regression using the Nadaraya-Watson estimator.

Reference(s):

Haerdle, W. (1990). Applied Nonparametric Regression. Econometric Society Monographs, No. 19. Cambridge University Press. Haerdle, W. (1991). Smoothing Techniques. With Implementations in S. Springer, New York, p. 220.

Usage:	`{mh, clo, cup} = regxcb(x {,h {,alpha {,K} {,v}}})`
Input:
	`x`	n x 2, the data. In the first column the independent and in the second column the dependent variable are contained.
	`h`	optional scalar, bandwidth. If not given, 20% of the range of x[,1] is used as default.
	`alpha`	optional scalar representing the confidence level; default alpha = 0.05.
	`K`	optional string, kernel function on [-1,1] with K(-1) = K(1) = 0; default K = "qua".
	`v`	optional m x 1 vector, values of the independent variable in which to compute the regression and the confidence bands. If not given, the (sorted) x is used.
Output:
	`mh`	n x 2 or m x 2 matrix; the first column represents the sorted first column of x or the sorted v and the second column contains the regression estimate on the values of the first column.
	`clo`	n x 2 or m x 2 matrix; the first column represents the sorted first column of x or the sorted v and 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 contains the sorted first column of x or the sorted v and the second one 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 quantlet "regcb" is recommended, which uses the faster WARPing method.

Example:

library("smoother") library("plot") x = read("motcyc") {mh, clo, cup} = regxcb(x,3) ; x =setmask( x,"cross") mh=setmask(mh,"line","blue") clo=setmask(clo,"line","blue","thin","dashed") cup=setmask(cup,"line","blue","thin","dashed") plot(x,mh,clo,cup)

Result:

Uniform confidence bands at confidence level
alpha = 0.05 are pictured using the bandwidth h = 0.3

Author: M. Mueller, 20020915