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: gam
See also: intest backfit

Quantlet: fastint
Description: fastint estimates the additive components and their derivatives of an additive model using a modification of the integration estimator plus a one step backfit, see Kim, Linton and Hengartner (1997) and Linton (1996)

Usage: m = fastint(x,y,h1,h2,loc{,xg})
Input:
x n x p matrix, the observed continuous explanatory variable, see also xg.
y n x q matrix, the observed response variables
h1 p x 1 vector or scalar, bandwidth for the pilot estimator. It is recommended to undersmooth here.
h2 pg x 1 vector or scalar, bandwidth for the backfit step. Here you should smooth in an optimal way.
loc {0,1,2}, degree of the local polynomial smoother used in the backfit step: 0 for Nadaraya Watson, 1 local linear, 2 local quadratic
xg ng x pg matrix, optional, the points on which the estimates shall be calculated. the columns of t and tg must have the same order up to column pg < = p. If grid is used, the results won t get centered!
Output:
m ng x pp matrix, where pp is pg*(loc+1). Estimates of the additive functions in column 1 to pg, the first derivatives in column (pg+1) to (2*pg) and the second derivatives in column (2*pg+1) to (3*pg).

Example:
library("gam")
randomize(1234)
n = 100
d = 2
; generate a correlated design:
var = 1.0
cov = 0.4  *(matrix(d,d)-unit(d)) + unit(d)*var
{eval, evec} = eigsm(cov)
t = normal(n,d)
t = t*((evec.*sqrt(eval)')*evec')
g1    = 2*t[,1]
g2    = t[,2]^2 -mean(t[,2]^2)
y     = g1 + g2  + normal(n,1) * sqrt(0.5)
h1    = 0.5
h2    = 0.7
loc   = 0
gest  = fastint(t,y,h1,h2,loc)
library("graphic")
pic   = createdisplay(1,2)
dat11 = t[,1]~g1
dat12 = t[,1]~gest[,1]
dat21 = t[,2]~g2
dat22 = t[,2]~gest[,2]
setmaskp(dat12,4,4,8)
setmaskp(dat22,4,4,8)
show(pic,1,2,dat11,dat12)
show(pic,1,1,dat21,dat22)

Result:
estimates of the additive functions



Author: W. Haerdle, S. Sperlich, 19970901 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006