In this paper a method for distributed detection for scenarios when there is no explicit knowledge of the probability models associated with the hypotheses is proposed. The underlying distributions are accurately learned from the data by bootstrapping. We propose using a nonparametric one-sample Anderson-Darling test locally at each sensor. The one-sample version of the test gives superior performance in comparison to the two-sample alternative. The local decision statistics, in particular p-values are then sent to a fusion center to make the final decision. This allows for fusing local independent test statistics even if they obey different distributions at each sensor. Three different methods of fusing p-vales from independent tests are considered. Our simulation results demonstrate that p-value fusion is a powerful approach, especially when the Fisher’s method is employed.