Series Estimation of Semilinear Models
Stephen Donald and
Whitney Newey
Journal of Multivariate Analysis, 1994, vol. 50, issue 1, 30-40
Abstract:
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 discrete distribution, features often present in applications. In addition, the smoothness conditions are quite weak: it will suffice for [radical sign]n consistency of [beta] that the modulus of continuity of g(z) and E[x z] be higher than one-fourth the dimension of z and that the number of terms be chosen appropriately.
Date: 1994
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