We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on \(L^2\)-distances of the empirical zero-bias transformation to the empirical distribution or the normal distribution function. Weak convergence results are derived under the null hypothesis, under contiguous as well as under fixed alternatives. A comparative finite-sample power study shows the competitiveness to classical procedures.

中文翻译：

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通过Stein表征中的分布固定点属性测试正态性

对于单变量正态性，我们提出了两个经典拟合优度检验系列。新过程基于经验零偏变换到经验分布或正态分布函数的\（L ^ 2 \） -距离。弱收敛结果是在原假设，连续以及固定替代条件下得出的。一项比较有限样本功效研究显示了其与经典程序的竞争优势。