Bridging the gap: A likelihood function approach for the analysis of ranking data

ABSTRACT

In the parametric setting, the notion of a likelihood function forms the basis for the development of tests of hypotheses and estimation of parameters. Tests in connection with the analysis of variance stem entirely from considerations of the likelihood function. On the other hand, non parametric procedures have generally been derived without any formal mechanism and are often the result of clever intuition. In the present article, we propose a more formal approach for deriving tests involving the use of ranks. Specifically, we define a likelihood function motivated by characteristics of the ranks of the data and demonstrate that this leads to well-known tests of hypotheses. We also point to various areas of further exploration such as how co-variates may be incorporated.

Keywords:

• Co-variates
• Friedman statistic
• Kruskal–Wallis test
• Likelihood function
• Neyman smooth tests
• Ranking data.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62G99
• 62F03