Studentisation upon rank-based linear estimators is generally considered an unnecessary topic, due to the domain restriction upon $S_{n}$, which exhibits constant variance. This assertion is functionally inconsistent with general analytic practice though. We introduce a general unbiased and minimum variance estimator upon the Beta-Binomially distributed Kemeny Hilbert space, which allows for permutation ties to exist and be uniquely measured. As individual permutation samples now exhibit unique random variance, a sample dependent variance estimator must now be introduced into the linear model. We derive and prove the Slutsky conditions to enable $t_{\nu}$-distributed Wald test statistics to be constructed, while stably exhibiting Gauss-Markov properties upon finite samples. Simulations demonstrate convergent decisions upon the two orthonormal Slutsky corrected Wald test statistics, verifying the projective geometric duality which exists upon the affine-linear Kemeny metric.

翻译：基于秩的线性估计量的学生化通常被视为一个不必要的话题，这是由于对$S_{n}$的域限制使其表现出恒定方差。然而，这一论断在功能上与一般分析实践并不一致。我们引入了一个基于Beta-二项分布Kemeny希尔伯特空间的通用无偏且最小方差估计量，该空间允许排列中存在结并对其进行唯一测量。由于单个排列样本现在表现出独特的随机方差，必须在线性模型中引入一个依赖于样本的方差估计量。我们推导并证明了斯卢茨基条件，从而能够构建$t_{\nu}$分布的沃尔德检验统计量，同时这些统计量在有限样本上稳定地表现出高斯-马尔可夫性质。模拟表明，基于两个正交的斯卢茨基校正的沃尔德检验统计量得出收敛的决策，验证了仿射线性Kemeny度量上存在的射影几何对偶性。