Library: | gam |
See also: | intest |
Quantlet: | pcad | |
Description: | pcad estimates the additive components, the significant directions and the regression on principal components |
Usage: | {jhat,g,mhat} = pcad(x,xg,y,h,bn) | |
Input: | ||
x | n x d matrix, the design | |
xg | ng x d matrix, the points where we want to estimate | |
y | n x 1 matrix, the response | |
h | d x 1 matrix or scalar, chosen bandwidth | |
bn | scalar, threshold for choosing significant directions | |
Output: | ||
jhat | q x 1 matrix, the set of significant directions | |
g | ng x q matrix, additive functions on principal components | |
mhat | ng x 1 matrix, estimate of regression using the significant functions |
library("gam") n = 100 v =uniform(n,4) x =v[,2:4] y =x[,1]^2+0.1*x[,2]+normal(n) h =0.5 bn=0.02 gest=pcad(x,x,y,h,bn) gest.jhat gest.g gest.mhat
The significant directions and the significant function, see Haerdle and Tsybakov "Additive Nonparametric Regression on Principal Components", J. Nonparametric Statist. (1994)157-84.