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

 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]
```estimates of the additive functions