**<Source Information**> Jin Seo Cho, Meng Huang, and Halbert L. White (2023): *Neural Computing & Applications*, 35 (2023), 21915-21934.

**<Abstract> ** In this paper, we study functional ordinary least squares estimator and its properties in testing the hypothesis of a constant zero mean function or an unknown constant non-zero mean function. We exploit the recent work by Cho, Phillips and Seo (2021) and show that the associated Wald test statistics have standard chi-square limiting null distributions, standard non-central chi-square distributions for local alternatives converging to zero at a $\sqrt{n}$ rate, and are consistent against global alternatives. These properties permit computationally convenient tests of hypotheses involving nuisance parameters. In particular, we develop new alternatives to tests for regression misspecification, that involves nuisance parameters identified only under the alternative. Our Monte Carlo simulations affirm the theory of the current study. Finally, we apply our methodology to the probit models for voting turnout that are estimated by Wolfinger and Rosenstone (1980) and Nagler (1991) and test whether the models are correctly specified or not.