Abstract
In Fortiana and Grané (J Stat Plann Infer 108:85–97), we study a scale-free statistic, based on Hoeffding’s maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper, we propose a scale-free adaptive statistic for testing exponentiality with optimal power against a specific alternative and obtain its exact distribution. An empirical power study shows that the test based on this new statistic has the same level of performance than the best tests in the statistical literature.
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Research project partially supported by Spanish grants SEJ2007-64500 and MTM2006-09920 (Ministry of Education and Science-FEDER).
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Grané, A., Fortiana, J. A directional test of exponentiality based on maximum correlations. Metrika 73, 255–274 (2011). https://doi.org/10.1007/s00184-009-0276-x
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DOI: https://doi.org/10.1007/s00184-009-0276-x