On combining the zero bias transform and the empirical characteristic\n function to test normality

2020/02/27 by Bruno Ebner, Ebner, Bruno
Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 62G10 #Secondary 62E10 #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2002.12085

openalex publication_date 2020/02/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We propose a new powerful family of tests of univariate normality. These\ntests are based on an initial value problem in the space of characteristic\nfunctions originating from the fixed point property of the normal distribution\nin the zero bias transform. Limit distributions of the test statistics are\nprovided under the null hypothesis, as well as under contiguous and fixed\nalternatives. Using the covariance structure of the limiting Gaussian process\nfrom the null distribution, we derive explicit formulas for the first four\ncumulants of the limiting random element and apply the results by fitting a\ndistribution from the Pearson system. A comparative Monte Carlo power study\nshows that the new tests are serious competitors to the strongest well\nestablished tests.\n

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