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Minimal-maximal correlation-type goodness-of-fit tests. (English) Zbl 1510.62218

Summary: In this paper we consider correlation-type tests based on plotting points which are modifications to the simultaneous closeness probability plotting points as recently introduced in the literature. In particular, we consider a maximal correlation test and a minimal correlation test. Furthermore, we provide two methods to carry out each test, where one method uses plotting points which are data dependent and the other test uses plotting points which are not. Some numerical properties on the associated correlation statistics are provided for various distributions, as well as a comprehensive power study to assess their performance in comparison to correlation-type tests based on more traditional plotting points. Two illustrative examples are also provided to demonstrate the tests. Finally, we make some observations and provide ideas for future work.

MSC:

62G30 Order statistics; empirical distribution functions
62G10 Nonparametric hypothesis testing
62N05 Reliability and life testing
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