Goodness of Fit Tests via Exponential Series Density Estimation

This paper explores the properties of a new nonparametric goodness of fit test, based on the likelihood ratio test of Portnoy (1988). It is applied via the consistent series density estimator of Crain (1974) and Barron and Sheu (1991). The asymptotic properties are established as trivial corollaries to the results of those papers as well as from similar results in Marsh (2000) and Claeskens and Hjort (2004). The paper focuses on the computational and numerical properties. Specifically it is found that the choice of approximating basis is not crucial and that the choice of model dimension, through consistent selection criteria, yields a feasible procedure. Extensive numerical experiments show that the usage of asymptotic critical values is feasible in moderate sample seizes. More importantly the new tests are shown to have significantly more power than established tests such as the Kolmogorov-Smirnov, Cramer-von Mises or Anderson-Darling. Indeed, for certain interesting alternatives the power of the proposed tests may be several times that of the established ones.