The nonparametric sign test dates back to the early 18th century with a data analysis by John Arbuthnot. It is an alternative to Gosset's more recent t-test for consistent differences between two sets of observations. Fisher's F-test is a generalization of the t-test to linear regression and linear null hypotheses. Only the sign test is robust to non-Gaussianity. Gutenbrunner et al. [1993] derived a version of the sign test for linear null hypotheses in the spirit of the F-test, which requires the difficult estimation of the sparsity function. We propose instead a new sign test called $\infty$-S test via the convex analysis of a point estimator that thresholds the estimate towards the null hypothesis of the test.

翻译：非参数符号检验可追溯至18世纪早期John Arbuthnot的数据分析工作。该检验作为Gosset近期提出的t检验的替代方法，用于检测两组观测值间的一致性差异。Fisher的F检验则是t检验向线性回归及线性零假设情形的推广。唯有符号检验对非高斯性具有稳健性。Gutenbrunner等人[1993]受F检验启发，推导出适用于线性零假设的符号检验变体，但该方法需对稀疏函数进行难以实现的估计。为此，我们提出一种称为$\infty$-S检验的新型符号检验，该方法通过对向检验零假设进行阈值估计的点估计量进行凸分析来实现。