Goodness of fit tests via exponential series density estimation

The properties of a new nonparametric goodness of fit test are explored. It is based on a likelihood ratio test, applied via a consistent series density estimator in the exponential family. The focus is on its 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 data-driven selection criteria, yields a feasible, parsimonious procedure. Numerical experiments show that the new tests have significantly more power than established tests, whether based upon the empirical distribution function, or alternate density estimators.