An innovative nonparametric ranking estimation method with multivariate binary variables

Abstract This paper proposes a novel nonparametric method for estimating the ranking of multivariate populations based on multivariate binary data. It consists of a two-step procedure: step 1 refers to a test of hypotheses for pairwise comparisons of C multivariate populations; step 2 concerns the ranking estimation based on the information provided by the p -values of the multivariate pairwise comparisons. The paper addresses the limitations of similar methods, which fail to control the Family-Wise Error Rate under multiple comparisons and, as a result, are likely to incorrectly reject the null hypothesis of equal populations when it is actually true, leading to an inaccurate ranking estimation. To demonstrate the effectiveness of the proposed approach, an extensive simulation study was conducted. The empirical relevance of the approach is illustrated through an original survey on Italian small and medium enterprises, aimed at ranking economic sectors according to their propensity to adopt Industry 4.0 technologies.