How to implement signed-rank wilcox.test() type procedures when a center of symmetry is unknown

The aim is twofold: (1) to indicate that the one-sample Wilcoxon signed rank test cannot be used directly when a center of symmetry is unknown; and (2) to propose and examine correct schemes for applying the Wilcoxon signed rank test with an estimated center of symmetry. It turns out that the Wilcoxon signed rank test and the sign test for symmetry do not provide valued outputs, when unknown centers of symmetry are estimated using underlying data. In such scenarios, these tests are not null-distribution-free and break down completely even based on samples with large numbers of observations. Theoretical propositions are shown to propose a simple correction of the corresponding R built-in function, employing p-value-based procedures. To perform the proposed algorithms, we develop new customized procedures for estimating the integrated squares of densities, probability weighted moments and special values of density functions. It is shown that the proposed testing strategies have Type I error rates under good control as well as exhibit high and stable power characteristics.