Goodness-of-fit tests and minimum distance estimation via optimal transformation to uniformity

A unified approach of parameter-estimation and goodness-of-fit testing is proposed. The new procedures may be applied to arbitrary laws with continuous distribution function. Specifically, both the method of estimation and the goodness-of-fit test are based on the idea of optimally transforming the original data to the uniform distribution, the criterion of optimality being an L2-type distance between the empirical characteristic function of the transformed data, and the characteristic function of the uniform ( 0 , 1 ) distribution. Theoretical properties of the new estimators and tests are studied and some connections with classical statistics, moment-based procedures and non-parametric methods are investigated. Comparison with standard procedures via Monte Carlo is also included, along with a real-data application.