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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