Stochastically weighted average conditional moment tests of functional form

We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments first presented in Bierens. We reduce the nuisance parameter space to known countable sets, which leads to a weighted average conditional moment test in the spirit of Bierens and Ploberger’s integrated conditional moment test (ICM). The weights are possibly stochastic in an arbitrary way, integer-indexed and flexible enough to cover a range of tests from average to higher quantile to maximum tests. The limit distribution under the null and local alternative belong to the same class as the ICM statistic, hence our test is admissible if the errors are Gaussian, and a flat weight leads to the greatest weighted average local power.