A goodness-of-fit test with nuisance parameters: Numerical performance (Q1598695)

\textit{J. Jurečková} and \textit{P.K. Sen} [ibid. 91, No. 2, 377-397 (2000; Zbl 0970.62025)] proposed goodness-of-fit tests for models admitting nuisance location or nuisance location and scale parameters, based on the difference of two estimators of the location parameter, that are asymptotically first-order equivalent iff the null hypothesis is true. We illustrate here the numerical performance of these tests on simulated data, demonstrating their applicability to practical problems. Comparisons are also made with the well-known Shapiro-Wilk goodness-of-fit test.