Tests of specification for parametric and semiparametric models

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 and sample selection 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.