Open AccessA General Class of Tests for Testing Homogeneity of Location Parameters against Umbrella Alternatives
Author(s) -
Manish Goyal,
Narinder Kumar
Publication year - 2018
Publication title -
international journal of mathematical, engineering and management sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 10
ISSN - 2455-7749
DOI - 10.33889/ijmems.2018.3.4-036
Subject(s) - homogeneity (statistics) , parametric statistics , statistical hypothesis testing , statistics , null hypothesis , mathematics , sample size determination , computer science , econometrics
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.