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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives

A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives

Manish Goyal
Department of Statistics, Panjab University, Chandigarh, India.

Narinder Kumar
Department of Statistics, Panjab University, Chandigarh, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2018.3.4-036

Received on January 26, 2018
  ;
Accepted on March 17, 2018

Abstract

In this paper, a general class of non-parametric tests for testing homogeneity of location parameter against umbrella alternatives is proposed. Testing for umbrella alternatives has many applications in the field of biology, medicine, botany, dose level testing, engineering, economics, psychology, zoology. As an example, the effectiveness of a drug is likely to increase with increase of dose up to a certain level and then its effect begins to decrease. The proposed test is based on linear combination of two-sample U-statistics. The null distribution of the test statistics is developed. We compare the test with some other competing tests in terms of Pitman asymptotic relative efficiency. To see execution of the test, a numerical example is provided. Simulation study is carried out to assess the power of proposed class of tests.

Keywords- Non-parametric tests, Umbrella alternatives, Null distribution, Pitman efficiency, Simulation study.

Citation

Goyal, M., & Kumar, N. (2018). A General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives. International Journal of Mathematical, Engineering and Management Sciences, 3(4), 498-512. https://dx.doi.org/10.33889/IJMEMS.2018.3.4-036.

Conflict of Interest

Acknowledgements

The authors thank anonymous reviewers for their valuable suggestions, which led to an improvement of the paper.

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