Is Rank Scaling Linear or none Linear? And Min/Max, is that scaled linear or not?
Rank is an ordinal variable by definition. It preserves order only and carries no information about scale or spacing. In practice, I don’t think the function–using rank as a variable–ends up being fully linear either. At least at the extreme ranks.
If this were truly a linear function, the top bucket would not stand out as such an extreme outlier. The fact that the highest-ranked bucket consistently shows a very large deviation indicates that the relationship is not linear, especially at the extremes. And most of the stocks we actually buy come from those extreme ranks.
So no — ranking is not linear in theory or in practice.
That said ,rank is a non-parametric transformation that often works well precisely because it ignores scale and magnitude. This can be a feature, and not a bug.
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