Nonparametric Methods in Statistics with SAS Applications

Chapter 5

Nonparametric Generalized Additive

Regression

5.1 Definition

A generalized additive model is an extension of a nonparametric linear regression

model. Suppose we obtain a sample of n independent observations of k predictor

variables x

1

,...,x

k

and a response y. A generalized additive regression model is used

to connect through a link function g(·) the mean response

µ

= E(y|x

1

,...,x

k

) and an

additive function of the predictors of the form s

0

+ s

1

(x

1

) + ···+ s

k

(x

k

) where s

0

is

the intercept, and s

1

(·),. . . , s

k

(·) are loess or univariate spline smoothers. The equa-

tion of the generalized additive model is

g(

µ

) = s

0

+ s

1

(x

1

) + ···+ s

k

(x

k

).

In this chapter ...