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)(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.