In this paper, we develop a simple non-parametric test for testing normal distribution based on the distance between empirical zero-bias transformation and empirical distribution. The asymptotic properties of the test statistic are studied. The finite sample performance of the proposed test is evaluated through a Monte Carlo simulation study. The power of our test is compared with several other tests for normality. We illustrate the test procedure using two real data sets. We also develop a jackknife empirical likelihood ratio test for standard normal distribution.

翻译：本文基于经验零偏变换与经验分布之间的距离，提出了一种检验正态分布的简单非参数方法。我们研究了检验统计量的渐近性质，并通过蒙特卡洛模拟评估了所提检验的有限样本表现。将本文检验的检验功效与其他几种正态性检验进行了比较，利用两个真实数据集说明了检验流程。此外，我们还开发了针对标准正态分布的刀切经验似然比检验。