  Statistical analysis in applied research, across almost every field (e.g.,
biomedical, economics, computer science, and psychological) makes use of
samples upon which the explicit error distribution of the dependent variable is
unknown or, at best, difficult to linearly model. Yet, these assumptions are
extremely common. Unknown distributions are of course biased when incorrectly
specified, compromising the generalisability of our interpretations -- the
linearly unbiased Euclidean distance is very difficult to correctly identify
upon finite samples and therefore results in an estimator which is neither
unbiased nor maximally informative when incorrectly applied. The alternative
common solution to the problem however, the use of non-parametric statistics,
has its own fundamental flaws. In particular, these flaws revolve around the
problem of order-statistics and the estimation in the presence of ties, which
often removes the introduction of multiple independent variables and the
estimation of interactions. We introduce a competitor to the Euclidean norm,
the Kemeny norm, which we prove to be a valid Banach space, and construct a
multivariate linear expansion of the Kendall-Theil-Sen estimator, which
performs without compromising the parameter space extensibility, and establish
its linear maximum likelihood properties. Empirical demonstrations upon both
simulated and empirical data shall be used to demonstrate these properties,
such that the new estimator is nearly equivalent in power for the glm upon
Gaussian data, but grossly superior for a vast array of analytic scenarios,
including finite ordinal sum-score analysis, thereby aiding in the resolution
of replication in the Applied Sciences.
