SFB 303 Discussion Paper No. A - 111
Author: Stoker, Thomas M.
Title: Nonparametric Tests of Additive Derivative Constraints
Abstract: This paper proposes nonparametric tests of additive constraints on the first and second derivatives of a
model E(y given x)=g(x), where the true function g is unknown. Such constraints are illustrated by the economic
restrictions of homogeneity and symmetry, and the statistical restrictions of additivity and linearity. The
proposed tests are based on estimates of regression coefficients, that statistically characterize the departures from
the constraint exhibited by the data. The coefficients are based on weighted average derivatives, that are
reformulated in terms of derivatives of the density of x. Coefficient estimators are proposed that use
nonparametric kernel estimators of the density and its derivatives. These statistics are shown to be square root of
N consistent and asymptotically normal, and thus suffer no efficiency loss from the nonparametric treatment of
the function g(x).
Creation-Date: March 1987
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