期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：1029
DOI：10.30757/ALEA.v18-38
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero bias transform. Limit distributions of the test statistics are provided under the null hypothesis, as well as under contiguous and fixed alternatives. Using the covariance structure of the limiting Gaussian process from the null distribution, we derive explicit formulas for the first four cumulants of the limiting random element and apply the results by fitting a distribution from the Pearson system. A comparative Monte Carlo power study shows that the new tests are serious competitors to the strongest well established tests.
其他关键词：Goodness-of-fit, Normal Distribution, Stein’s Method, Zero Bias Transformation, Empirical Characteristic Function.
