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By using nonparametric kernel estimation method and a central limit theorem for degenerate U-statistics of order higher than two, the authors develop several consistent model specification tests in the context of a nonparametric regression model. These include tests for omitted variables, tests for a partially linear model, and tests for a semiparametric single index model. The asymptotic normality of the test statistics are established under the respective null hypotheses and consistent estimators of the asymptotic variances are provided. Copyright 1996 by The Econometric Society.
Fan et al. (Mon,) studied this question.