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On the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests

On the automatic selection of the tuning parameter appearing in certain families of goodness-of-fit tests

The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics, indexed by a parameter λ∈Λ, is available to test the goodness of fit of F, the underlying distribution function of a set of independent real-valued random variables, to a location-scale/scale family of …