Nonparametric multiple sample scale testing using U-statistics. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Goyal, Manish; Kumar, Narinder
• Is Part Of: Communications in statistics. Volume 49:Issue 11(2020)
• Page Start: 3019
• Page End: 3027
• Publication Date: 2020-11-01
• Subjects: Nonparametric tests -- Scale parameters -- U-statistics -- Asymptotic relative efficiency -- Simulation study; 62E20 -- 62G10 -- 62G30 -- 62P10; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1532002
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: Testing of equality of scale parameters is one of the fundamental problems in Statistics and is useful in many fields such as agriculture, engineering, experimental methods and dose level testing. In this paper, we propose a new class of nonparametric tests, to test whether the scale parameters of all the populations are equal, or there is an umbrella ordering in the scale parameters. The proposed test is based on weighted linear combination of two-sample U -statistics. The optimal choice of weights is determined so that proposed tests have maximum efficiency. The comparison of proposed test with respect to existing tests is made in terms of Pitman asymptotic relative efficiency. A numerical example is provided for illustrative purpose. Power of the proposed test is also assessed using Monte Carlo simulation study.