Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms
在非参数回归模型框架下，开发了多个一致的检验方法，包括检验部分回归变量是否显著，以及检验半参数函数形式（如部分线性模型和单指标模型）是否正确，这些检验基于高阶退化U统计量的中心极限定理，无需样本分割或随机加权等临时修正，且备择假设下检验统计量发散速度更快。
In this paper, we develop several consistent tests in the context of a nonparametric regression model. These include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function, where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative. One common feature to the construction of all these tests is the use of the Central Limit Theorem for degenerate U-statistics of order higher than two. As a result, they share the same advantages over most of the corresponding existing tests in the literature: (a) They do not depend on any ad hoc modifications such as sample splitting, random weighting, etc. (b) Under the alternative hypotheses, the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications.