Timeline for Reference to iterated logarithm law and Smirnov law of empirical CDF
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2015 at 22:45 | vote | accept | Yan Zhu | ||
| Aug 27, 2015 at 20:29 | comment | added | P.Windridge | A pedagogical comment: The Smirnov (von Mises - Cramer) statistic uses the integral of the squared empirical process, whereas the Kolmogorov-Smirnov statistic uses the maximum absolute value of the EP. | |
| Aug 27, 2015 at 20:15 | answer | added | P.Windridge | timeline score: 1 | |
| Aug 27, 2015 at 20:06 | comment | added | P.Windridge | Here is an article that summarises the proof I suggested above = projecteuclid.org/euclid.aop/1020107767 (the pdf is open access, projecteuclid.org/download/pdf_1/euclid.aop/1020107767) | |
| Aug 27, 2015 at 19:52 | comment | added | P.Windridge | This looks might it may contain hints-> epubs.siam.org/doi/abs/10.1137/1119082 but I don't have access. It makes the useful point that you only need to consider the uniform[0,1] distribution (assuming $F$ is continuous). I guess the easiest proof would proceed by writing the statistic in terms of the empirical process, using the fact that that converges to a Gaussian process, and then using something about the distribution of the latter. But this is just idle speculation :) | |
| Aug 27, 2015 at 19:24 | comment | added | P.Windridge | Note the statistic appearing in the Smirnov Law is better known as the Cramer-von Mises statistic (or Cramer-von Mises-Smirnov). | |
| Aug 17, 2015 at 9:42 | history | edited | Davide Giraudo | CC BY-SA 3.0 |
edited tags; edited title
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| Aug 17, 2015 at 3:26 | answer | added | Zurab Silagadze | timeline score: 3 | |
| Aug 17, 2015 at 3:01 | history | edited | Yan Zhu | CC BY-SA 3.0 |
some typos
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| Aug 15, 2015 at 22:24 | history | asked | Yan Zhu | CC BY-SA 3.0 |