An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives. (3rd March 2021)

• Record Type: Journal Article
• Authors: Marange, Chioneso Show; Qin, Yongsong
• Other Names: Psaradakis Zacharias Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2021(2021)
• Publication Date: 2021-03-03
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2021/6661985
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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.