Mathematical Sciences: Interblock Rank Tests

该研究涉及对单变量和多变量因子设计统计中的块间秩检验的研究，其中所有相关数据在不考虑块或变量隶属度的情况下进行排序。该研究将包括对某些块间秩统计的小样本属性、效率和鲁棒性属性与对齐秩检验、秩变换程序和块内秩检验的相应属性的比较。这将推广到一般替代下具有相关数据的线性秩统计量的渐近性质。还将研究从排列度量产生块内秩检验的某些方法的扩展，以包括新的块间秩检验。

The research involves the study of interblock rank tests in statistics for univariate and multivariate factorial designs in which all of the dependent data is ranked without regard to block or variate membership. The study will include a comparison of the small sample properties, efficiency, and robustness properties of certain interblock rank statistics with the corresponding properties of aligned rank tests, rank transform procedures and intrablock rank tests. This will be extended to the asymptotic properties of linear rank statistics with dependent data under general alternatives. Research will also be conducted on the extension of certain approaches of generating intrablock rank test from metrics on permutations to include new interblock rank tests.