1. Modifications to the Jarque–Bera Test.
- Author
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Glinskiy, Vladimir, Ismayilova, Yulia, Khrushchev, Sergey, Logachov, Artem, Logachova, Olga, Serga, Lyudmila, Yambartsev, Anatoly, and Zaykov, Kirill
- Subjects
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MONTE Carlo method , *GAUSSIAN distribution , *STATISTICAL hypothesis testing , *KURTOSIS , *UNDERGRADUATES - 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, α = 0.05 and α = 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), Cramér–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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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