Timeline for Why can't one generalize the Kolmogorov-Smirnov test to 2 or more dimensions?
Current License: CC BY-SA 3.0
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| May 27, 2014 at 23:24 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 23:04 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 23:01 | comment | added | whuber♦ | (+1) Thank you very much, Glen, for broadening this reply and making it more nuanced. Although I find the OP's reference of dubious quality (at the outset it misinterprets what hypothesis tests mean), it finally admits that "the bootstrap can come to the rescue, and significance levels for the particular multidimensional statistic and the particular dataset under study can be numerically computed." This seems aligned, at least in spirit, with how your answer is shaping up. | |
| May 27, 2014 at 22:54 | comment | added | Glen_b | @whuber I've made substantial changes in the light of your very kind response to my error. I will likely make further changes as I add references and more details in the hopes of making an answer that will be more useful in the longer term. | |
| May 27, 2014 at 22:46 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 21:21 | comment | added | whuber♦ | I do not fully understand this answer. I imagine many astronomical datasets (as well as many other small-dimensional datasets) do not come with intrinsically meaningful coordinate systems. Thus your claim that the points are "ordered already" would be invalid in such circumstances. It could be rescued if you were able to show that the KS statistic is independent of the coordinates used to identify the locations. I don't think that's true in two or more dimensions, but I could be mistaken. | |
| May 27, 2014 at 21:07 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 12:21 | vote | accept | pedrofigueira | ||
| May 27, 2014 at 10:51 | comment | added | Glen_b | Certainly - though it depends on what alternatives are of interest. | |
| May 27, 2014 at 10:11 | comment | added | kjetil b halvorsen♦ | This answer is clearly correct, but beware: that the KS test can be used, doesnt mean it should be used. Usually there are far better tests (more powerfull) ones. | |
| May 27, 2014 at 2:46 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 2:41 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 2:20 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 1:45 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 1:40 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 1:29 | history | edited | Glen_b | CC BY-SA 3.0 |
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| May 27, 2014 at 1:23 | history | answered | Glen_b | CC BY-SA 3.0 |