An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives
An omnibus test for normality with an adjustment for symmetric alternatives is developed using the empirical likelihood ratio technique. We first transform the raw data via a jackknife transformation technique by deleting one observation at a time. The probability integral transformation was then ap...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2021/6661985 |
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| _version_ | 1832567747562700800 |
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| author | Chioneso Show Marange Yongsong Qin |
| author_facet | Chioneso Show Marange Yongsong Qin |
| author_sort | Chioneso Show Marange |
| collection | DOAJ |
| description | An omnibus test for normality with an adjustment for symmetric alternatives is developed using the empirical likelihood ratio technique. We first transform the raw data via a jackknife transformation technique by deleting one observation at a time. The probability integral transformation was then applied on the transformed data, and under the null hypothesis, the transformed data have a limiting uniform distribution, reducing testing for normality to testing for uniformity. Employing the empirical likelihood technique, we show that the test statistic has a chi-square limiting distribution. We also demonstrated that, under the established symmetric settings, the CUSUM-type and Shiryaev–Roberts test statistics gave comparable properties and power. The proposed test has good control of type I error. Monte Carlo simulations revealed that the proposed test outperformed studied classical existing tests under symmetric short-tailed alternatives. Findings from a real data study further revealed the robustness and applicability of the proposed test in practice. |
| format | Article |
| id | doaj-art-a8d37d44006842fbadbe1aebfe15b90c |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-a8d37d44006842fbadbe1aebfe15b90c2025-02-03T01:00:41ZengWileyJournal of Probability and Statistics1687-952X1687-95382021-01-01202110.1155/2021/66619856661985An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric AlternativesChioneso Show Marange0Yongsong Qin1Department of Statistics, Faculty of Science and Agriculture, Fort Hare University, East London Campus, East London 5201, South AfricaDepartment of Statistics, Faculty of Science and Agriculture, Fort Hare University, Alice Campus, Alice 5700, South AfricaAn omnibus test for normality with an adjustment for symmetric alternatives is developed using the empirical likelihood ratio technique. We first transform the raw data via a jackknife transformation technique by deleting one observation at a time. The probability integral transformation was then applied on the transformed data, and under the null hypothesis, the transformed data have a limiting uniform distribution, reducing testing for normality to testing for uniformity. Employing the empirical likelihood technique, we show that the test statistic has a chi-square limiting distribution. We also demonstrated that, under the established symmetric settings, the CUSUM-type and Shiryaev–Roberts test statistics gave comparable properties and power. The proposed test has good control of type I error. Monte Carlo simulations revealed that the proposed test outperformed studied classical existing tests under symmetric short-tailed alternatives. Findings from a real data study further revealed the robustness and applicability of the proposed test in practice.http://dx.doi.org/10.1155/2021/6661985 |
| spellingShingle | Chioneso Show Marange Yongsong Qin An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives Journal of Probability and Statistics |
| title | An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives |
| title_full | An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives |
| title_fullStr | An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives |
| title_full_unstemmed | An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives |
| title_short | An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives |
| title_sort | empirical likelihood ratio based omnibus test for normality with an adjustment for symmetric alternatives |
| url | http://dx.doi.org/10.1155/2021/6661985 |
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