Nonparametric Methods in Statistics with SAS Applications

Chapter 4

Nonparametric Regression

For some data sets it is impossible to describe the relation between the response vari-

able y and predictor variables x

1

,...,x

k

by a function of an a priori known form (for

example, polynomial or exponential). A useful tool in this case is a nonparametric

regression, specified by

y = f (x

1

,...,x

k

) +

ε

(4.1)

where f is a nonparametric response function with no explicit functional form, and

ε

’s are independent identically distributed random errors with a zero mean and con-

stant variance

σ

2

. No assumption is made on the form of the probability distribution

of

ε

’s.

As an illustration, consider the following scatterplot of a