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Validation tests for semi-parametric models

Tests are proposed for validation of the hypothesis that a partial linear regression model adequately describes the structure of a given data set. The test statistics are formulated following the approach of Fourier-type conditional expectations first suggested by Bierens [Consistent model specification tests. J Econometr. 1982;20:105–134]. The proposed procedures are computationally convenient, and under fairly mild conditions lead to consistent tests. Corresponding bootstrap versions are compared with alternative procedures for a wide selection of different estimators of the underlying partial linear model.