Before revision:  The test is simple to implement, because it requires estimating only the restricted semiparametric model and because the asymptotic distribution of the test statistic is pivotal. The projection interpretation of series estimators allows me to derive a degrees of freedom correction.
After revision:  The test is asymptotically standard normal under the null. Compared with the earlier literature on series-based specification tests in parametric models, I rely on the projection property of series estimators allows me to derive a degrees of freedom correction.