XploRe Help : lregestp

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:	regestp lpregest lregxestp

Quantlet:		lregestp
Description:		estimates a multivariate regression function using local linear kernel regression. The computation uses WARPing.

Reference(s):

Local Polynomial Fitting, Ruppert/Wand (1995) Binning for local polynomials, Fan/Marron (1994) WARPing method, W. Haerdle, "Smoothing Techniques with applications in S"

Usage:	`mh = lregestp(x {,h {,K {,d}}})`
Input:
	`x`	n x (p+1), the data. They contain the independent variables in the first p columns and the dependent variable in the last column.
	`h`	scalar or p x 1 vector, bandwidth. If not given, 20% of the volume of x[,1:p] is used.
	`K`	string, kernel function on [-1,1]^p. If not given, the product Quartic kernel "qua" is used.
	`d`	scalar, discretization binwidth. d[i] must be smaller than h[i]. If not given, the minimum of h/3 and (max(x)-min(x))'/r, with r=100 for p=1, and r=(1000^(1/p)) for p>1 is used.
Output:
	`mh`	m x (p+1) matrix, the first p columns constitute a grid and the last column contains the regression estimate on that grid.

Note:

The WARPing enhances the speed of computation, but may lead to computational errors, if the bandwidth is small. For p<=2 WARPing is usually faster than exact computation. For p>2, the macro "regxestp" should be used instead.

Example:

library("smoother") library("plot") ; x = 4.*pi.*(uniform(400,2)-0.5) m = sum(cos(x),2) e = uniform(400)-0.5 x = x~(m+e) ; mh = regestp(x,2) mh = setmask(mh, "surface","blue") m = setmask(x[,1:2]~m,"black","cross","small") plot(mh,m) setgopt(plotdisplay,1,1,"title","ROTATE!")

Result:

The Local Linear regession estimate (blue) using
Quartic kernel and bandwidth h=2 and the true
regression function (thin black crosses) are pictured.

Author: M. Mueller, 20010529