  A framework for estimation and hypothesis testing of functional restrictions
against general alternatives is proposed. The parameter space is a reproducing
kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a
parametric model. The test allows us to deal with infinite dimensional nuisance
parameters. The methodology is based on a moment equation similar in spirit to
the construction of the efficient score in semiparametric statistics. The
feasible version of such moment equation requires to consistently estimate
projections in the space of RKHS and it is shown that this is possible using
the proposed approach. This allows us to derive some tractable asymptotic
theory and critical values by fast simulation. Simulation results show that the
finite sample performance of the test is consistent with the asymptotics and
that ignoring the effect of nuisance parameters highly distorts the size of the
tests.
