Modifications to the Jarque-Bera Test

Author(s)

Glinskiy, Vladimir ; Ismayilova, Yulia ; Khrushchev, Sergey ; Logachov, Artem ; Logachova, Olga ; Serga, Lyudmila ; Yambartsev, Anatoly ; Zaykov, Kirill

• Document type: Journal article
• Source: MATHEMATICS; v. 12, n. 16, p. 16-pg., 2024-08-01.

Abstract

The Jarque-Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, alpha=0.05 and alpha=0.01, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Cram & eacute;r-von Mises (CVM), Lilliefors (LF), and Shapiro-Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes n=25,50,75,100,150,200,250,500, and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera. (AU)

• FAPESP's process: 23/13453-5 - Stochastic systems modeling
• Grantee: Luiz Renato Gonçalves Fontes
• Support Opportunities: Research Projects - Thematic Grants