This paper discusses estimation of the semilinear model E[y \ x, z] =
x'beta + g(z) using series approximations to the unknown function g(z)
under much weaker conditions than heretofore given in the literature.
In particular, we allow for z being multidimensional and to have a di
screte distribution, features often present in applications. In additi
on, the smoothness conditions are quite weak: it will suffice for squa
re-root n consistency of beta that the modulus of continuity of g(z) a
nd E[x \ z] be higher than one-fourth the dimension of z and that the
number of terms be chosen appropriately. (C) 1994 Academic Press, Inc.