The Uniformly More Powerful Tests than the Likelihood Ratio Test Using Intersection-Union Hypotheses for Variance of Independent Samples from Normal Distribution

Nicknam, Zahra; Chinipardaz, Rahim

doi:10.61186/jss.19.1.4

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The Uniformly More Powerful Tests than the Likelihood Ratio Test Using Intersection-Union Hypotheses for Variance of Independent Samples from Normal Distribution

Zahra Nicknam

, Rahim Chinipardaz ^*

Abstract: (419 Views)

Classical hypothesis tests for the parameters provide suitable tests when the hypotheses are not restricted. The best are the uniformly most powerful test and the uniformly most powerful unbiased test. These tests are designed for specific hypotheses, such as one-sided and two-sided for the parameter. However, in practice, we may encounter hypotheses that the parameters under test have typical restrictions in the null or alternative hypothesis. Such hypotheses are not included in the framework of classical hypothesis testing. Therefore, statisticians are looking for more powerful tests than the most powerful ones. In this article, the union-intersection test for the sign test of variances in several normal distributions is proposed and compared with the likelihood ratio test. Although the union-intersection test is more powerful, neither test is unbiased. Two rectangular and smoothed tests have been examined for a more powerful test.

Keywords: Intersection-:union: test, Likelihood ratio test, More powerful test, Rectangle test, Smoother test

Full-Text [PDF 752 kb] (257 Downloads)

Type of Study: Research | Subject: Statistical Inference
Received: 2024/05/26 | Accepted: 2024/08/31

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