This paper provides a general framework for constructing speciﬁcation tests for parametric and semiparametric models. The paper develops new speciﬁcation tests using the general framework. In particular, speciﬁcation tests for semiparametric partially linear regression, sample selection, and censored regression models are introduced. The results apply in time series and cross-sectional contexts. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes.
Whang, Yoon-Jae and Andrews, Donald W.K., "Tests of Specification for Parametric and Semiparametric Models" (1991). Cowles Foundation Discussion Papers. 1211.