XploRe Help : locpolex

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:	locpol

Quantlet:		locpolex
Description:		computes the local polynomial estimator with an arbitrary kernel.

Usage:	`{ab,e} = locpolex(x,xg,y,h{,kernfunc,omitx,z,zg})`
Input:
	`x`	n x d matrix of explanatory variables
	`xg`	m x d matrix of grid points at which the estimation will be done
	`y`	n x 1 vector representing the dependent variable
	`h`	scalar or d x 1 vector representing the bandwidth(s); if h is a scalar, the same bandwidth is used across all dimensions of x
	`kernfunc`	optional string, it contains the name of a function that computes a kernel (e.g., a function from library "kernel"); if kernfunc is omitted or empty, the Gaussian kernel function "gau" is used
	`omitx`	optional scalar, if non-zero, then the point at which we just compute the local linear approximation is itself excluded from the computation; this option is only usable if x == xg and it is disabled (omitx == 0) by default
	`z`	optional n x d1 matrix, it can contain alternative data points that are then used in computing the kernel distances instead of x (e.g., z can be a subset of x); it can be used only together with zg; by default, z = x
	`zg`	optional m x d1 matrix, it can contain alternative data points that are then used in computing the kernel distances instead of xg (e.g., z can be a subset of x); it can be used only together with z; by default, zg = xg
Output:
	`ab`	m x (d+1) matrix, the regression function (the first column) and its first d derivatives at xg
	`e`	n x 1 vector of regression residuals

Note:

1) It is possible to include only linear terms in locpolex, not quadratic ones.

2) Locpolex is more flexible: a user can choose a kernel function and can also use kernel distances computed from observations different from x (e.g., kernel is applied on a subspace of data x). Moreover, regression residuals are computed. These features are used, for example, by MIregest quantlet.

Example:

library("smoother") library("plot") ; generate data n = 200 x = sort(2*uniform(n)) y = 1.5*cos(x^3) + 0.2 * normal(n) h = 0.1 ; estimation with gaussian and quartic kernel mh1 = locpolex(x,x,y, h) mh2 = locpolex(x,x,y, h, "qua") ; plot data = setmask(x ~ y, "small") lp1 = setmask(x ~ mh1.ab[,1], "line", "thin", "red") lp2 = setmask(x ~ mh2.ab[,1], "line", "thin", "blue") plot(data, lp1, lp2)

Result:

A display showing local polynomial regression with the
Gaussian (red line) and the quartic (blue line) kernels.

Author: P. Cizek, 20020419