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

• Autor(a) principal: Tenreiro, Carlos
• Data de Publicação: 2019
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/87197; https://doi.org/10.1080/00949655.2019.1598409
• topic: goodness-of-fit tests; data-based tuning parameter selection; calibration; normality tests; empirical characteristic function; exponentiality tests; empirical Laplace transform

The situation, common in the current literature, is that of a whole family of location-scale/scale invariant test statistics, indexed by a parameter $\lambda\in\Lambda$, 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 distribution functions. The power properties of the tests associated with the different statistics usually depend on the parameter $\lambda$, called the ``tuning parameter'', which is the reason that its choice is crucial to obtain a performing test procedure. In this paper, we address the automatic selection of the tuning parameter when $\Lambda$ is 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 into a single test procedure is applied to well known families of test statistics for normality and exponentiality. A simulation study is carried out to access the power of the different tests under consideration, and to compare them with the fixed tuning parameter procedure, usually recommended in the literature.