We introduce generalized probability-probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real-valued data. These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P plots and are distribution-free under the null hypothesis. We also define the generalized P-P plot process and the corresponding, consistent tests. The behaviour of the tests under contiguous alternatives is studied in detail; in particular, limit theorems for the generalized P-P plot processes are presented. By their structure, the tests perform very well for spike (or pulse) alternatives. We also study the finite sample properties of the tests through a simulation study.

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Keywords Contiguous alternative, Generalized P-P plot, Goodness-of-fit, Limit theorem, Two-sample problem
Persistent URL dx.doi.org/10.1016/j.jspi.2006.06.006, hdl.handle.net/1765/36123
Journal Journal of Statistical Planning and Inference
Mushkudiani, N, & Einmahl, J.H.J. (2007). Generalized probability-probability plots. Journal of Statistical Planning and Inference, 137(3), 738–752. doi:10.1016/j.jspi.2006.06.006