Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form

We develop a consistent conditional moment test of Lp-best predictor functional form, 1<p<=2. Our main result is a reduction of the nuisance parameter space to the set of integers which greatly simplifies asymptotic theory, and allows for removal of the nuisance parameter in a mechanical fashion. Our results provide a fresh vantage into why Bierens’ (1990) moment condition works, and uncovers a new class of weights which sharply contrasts with Stinchcombe and White’s (1997) weight classification (real analytic and non-polynomial). The computation of a weighted-Average CM statistic is easy and asymptotically nuisance parameter free be cause it incorporate s all possible nuisance paramete r values. Our test serves as a consistent model check in Lp-regression environments. Finally, we provide a simple nuisance parameter free series expansion of the best Lp-predictor.