Statistically Equivalent Blocks in Multivariate Hypothesis Testing with Applications to Life-testing

Music City Center 

Multivariate hypothesis testing is fundamental in modern data analysis, particularly in high-dimensional settings. This work revisits the concept of statistically equivalent blocks and demonstrates how it can be used to generalize several classical nonparametric tests beyond the univariate setting. The proposed generalization preserves important testing properties without relying on spatial ranks or data depth. A key application is the reformulation of the precedence test using statistically equivalent blocks, leading to a multivariate nonparametric procedure suitable for lifetime data. This test accommodates certain types of censoring, making it particularly relevant for life-testing applications. In addition to reviewing the literature on statistically equivalent blocks in hypothesis testing, we compare the proposed approach with some existing multivariate nonparametric methods and discuss its advantages.

Nonparametric Testing

Distribution-Free

Multivariate

Life-testing

Statistically Equivalent Blocks

Two-Sample 

Section on Nonparametric Statistics