Jonckheere Type Test Procedure with Optimal Criterion Under Order Restrictions

SYNOPTIC ABSTRACT

In many practical applications, there is a need for testing of an hypothesis under order restrictions. We propose a general class of tests which generalizes the tests proposed by Jonckheere (1954), Kumar et al. (1994a, b), and Patil (2007). The asymptotic distribution of test statistic under null hypothesis, as well as under an equally spaced sequence of local alternatives, is derived. Pitman asymptotic relative efficiency comparisons with respect to competing tests are made to evaluate the performance of the proposed class of tests. An example is provided in Hundal (1969) data for implementing the proposed test procedure. Furthermore, a simulation study is carried out to estimate the power and level of significance of the proposed class of tests.

KEYWORDS AND PHRASES:

• Asymptotic power
• optimality criterion
• restricted alternatives
• simulation study
• sub-sample

Acknowledgments

The authors thank Professor Madhuri S. Mulekar, Editor-in-Chief, and an anonymous referee for their valuable suggestions, which led to an improvement of the article.

Additional information

Funding

The first author acknowledges partial assistance provided under the Promotion of University Research and Scientific Excellence (DST-PURSE) programme, and the second author acknowledges support provided by University Grants Commission, New Delhi through Junior Research Fellowship.