Title: Data-based selection of the tuning parameter appearing in certain families of goodness-of-fit tests
Authors: Carlos Tenreiro - University of Coimbra (Portugal) [presenting]
Abstract: The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics indexed by a set $\Lambda$ of real numbers, is available to test the goodness of fit of $F$, the underlying distribution function of the real-valued iid random variables, to a location-scale/scale family of distribution functions. The power properties of the tests associated with the different statistics usually depend on $\lambda\in\Lambda$, called the ``tuning parameter'', which is the reason that its choice is crucial to obtain a performing test procedure. We address the data-dependent choice of $\lambda$ in the set $\Lambda$, assumed to be finite, as well as the calibration of the associated goodness-of-fit test procedure. Examples of existing and new tuning parameter selectors are discussed, and the methodology presented, of combining different test statistics in a single test procedure, is applied to well-known families of test statistics for normality and exponentiality.