4 ms·

This sounds like nonsense. We're talking about multivariate distributions, and you haven't defined a norm by which ordinal comparisons can be made between sampl

This sounds like nonsense. We're talking about multivariate distributions, and you haven't defined a norm by which ordinal comparisons can be made between sample points.

brewmarche 4y ago
All norms on finite-dimensional vector spaces are equivalent so the choice of norm shouldn’t matter for tails really.
- hgsgm 4y ago
  Norms are equivalent in the sense they differ by less than a constant in both directions, not in the sense that outliers are the same in all norms.
  - brewmarche 4y ago
    Norms are for dealing with magnitude not direction (and were brought up by my parent commenter). If you care about direction specify an angle, quadrant, cone or other subregion that allows you to take the limit to infinity which then doesn’t depend on the norm. Note this is the same in the univariate case where we talk about left and right tail if we need to distinguish.
- TreeRingCounter 4y ago
  > All norms on finite-dimensional vector spaces are equivalent How are you going to tell me that an L1 norm is equivalent to an L2 norm, for example?
  - brewmarche 4y ago
    This is a standard result which you can look up in most text books, or here on StackExchange: https://math.stackexchange.com/questions/57686/understanding-of-the-theorem-that-all-norms-are-equivalent-in-finite-dimensional https://math.stackexchange.com/questions/57686/understanding... In the end it doesn’t whether we go to infinity in one norm or the other. Note that I am talking about finite dimensions, so I guess you didn’t mean the L^p norms or \ell^p for integrable functions or sequences but the finite-dimensional p-norms.
    - TreeRingCounter 4y ago
      This theorem is completely irrelevant - the equivalence relation described by the theorem does not imply an equivalence between ordinal relationships imposed by different choice of norm. Also, "tails" isn't the same as "at infinity".

This sounds like nonsense. We're talking about multivariate distributions, and you haven't defined a norm by which ordinal comparisons can be made between sample points.

brewmarche 4y ago

All norms on finite-dimensional vector spaces are equivalent so the choice of norm shouldn’t matter for tails really.

hgsgm 4y ago
Norms are equivalent in the sense they differ by less than a constant in both directions, not in the sense that outliers are the same in all norms.
- brewmarche 4y ago
  Norms are for dealing with magnitude not direction (and were brought up by my parent commenter). If you care about direction specify an angle, quadrant, cone or other subregion that allows you to take the limit to infinity which then doesn’t depend on the norm. Note this is the same in the univariate case where we talk about left and right tail if we need to distinguish.
TreeRingCounter 4y ago
> All norms on finite-dimensional vector spaces are equivalent How are you going to tell me that an L1 norm is equivalent to an L2 norm, for example?
- brewmarche 4y ago
  This is a standard result which you can look up in most text books, or here on StackExchange: https://math.stackexchange.com/questions/57686/understanding-of-the-theorem-that-all-norms-are-equivalent-in-finite-dimensional https://math.stackexchange.com/questions/57686/understanding... In the end it doesn’t whether we go to infinity in one norm or the other. Note that I am talking about finite dimensions, so I guess you didn’t mean the L^p norms or \ell^p for integrable functions or sequences but the finite-dimensional p-norms.
  - TreeRingCounter 4y ago
    This theorem is completely irrelevant - the equivalence relation described by the theorem does not imply an equivalence between ordinal relationships imposed by different choice of norm. Also, "tails" isn't the same as "at infinity".