Use non-parametric techniques to validate the model

A statistician once said that parametric statistics finds exact solutions to ‘approximate
problems’, while non-parametric statistics finds approximate solutions to ‘exact
problems’. Non-parametric tests make very few assumptions, and are generally much
more powerful and easier to understand than parametric tests. In addition, nonparametric
statistics often involve less computational work and are easier to apply
than other statistical techniques. Therefore, they should be used whenever possible
to validate or invalidate the parametric assumptions.
Their results may sometimes be surprising. For instance, Ait-Sahalia (1996a,b)
estimates the diffusion coefficient of the US short-term interest rate non-parametrically
by comparing the marginal density implied by a set of models with the one
implied by the data, given a linear specification for the drift. His conclusions are that
the fit is extremely poor. Indeed, the non-parametric tests reject ’every parametric
model of the spot rate previously proposed in the literature’, that is, all linear-drift
short-term interest rate models!