Timeline for Rate of convergence of uniform order statistics to their expectations
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2017 at 15:30 | vote | accept | Chee | ||
| Apr 15, 2017 at 12:47 | comment | added | Chee | Hi Henry, your example is very illuminating and can be modified to illustrate the more extreme case where the maximal spacing is very close to zero but the KS norm is very very close to 1. | |
| Apr 15, 2017 at 12:20 | vote | accept | Chee | ||
| Apr 21, 2017 at 15:30 | |||||
| Apr 15, 2017 at 11:37 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 15, 2017 at 11:06 | comment | added | Henry.L | @Chee Regarding your new question, "Why is the maximal uniform spacing so small in magnitude compared to the maximal oscillation in the empirical distribution?"see my updates. For the second part " Which rate of convergence would you use to identify the locations of uinform(uniform) order statistics?" I believe it would be a prolonged discussion that depends on the specific situation you are facing, so via emails? | |
| Apr 15, 2017 at 2:28 | comment | added | Chee | Hi Henry, I updated the post as I found the rate of convergence of uniform order statistics, which is induced by a theorem of K.L. Chung. As a follow up, I raised a question on the relationship between maximal uniform spacing, maximal deviation of empirical distribution, and cannonical locations of uniform order statistics. Any comments? | |
| Apr 12, 2017 at 21:49 | comment | added | Chee | thank you! I will digest all you comments as much as possible and follow up once I found something "new" to the post. PS. I did not read the technical part of Talagrand's paper but was attacted by the elegance and power of his ideas exposed there. :) | |
| Apr 12, 2017 at 21:43 | comment | added | Henry.L | @Chee It is simple. If concentration of measures occur in the tail, then the bound fails. So most tail bounds require Guassian/sub-Gaussian assumptions. PS: I never think Talagrand's work can be understood via a "quick look"....but since you mentioned his work, the chaining is a general technique that can be used to bound the tail, but the bound is given by another process instead of convergence behavior. An easier ref is Rigollet OR Vershynin(www-personal.umich.edu/~romanv/teaching/2015-16/626/…) You may also find some of my old answers interesting. | |
| Apr 12, 2017 at 21:28 | comment | added | Chee | Hi Henry, thank you a lot for providing references and suggestions! Could you please give a quick explanation on why "For a general distribution family, it is almost impossible to obtain a tail-bound on the order statistics due to the concentration of measures phenomenon"? I am very new to the study of order statistics and U-statistics, and attracted after quickly reading Talagrand's Ann. Prob. article "A new look at independent" | |
| Apr 12, 2017 at 21:03 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Apr 12, 2017 at 20:58 | history | answered | Henry.L | CC BY-SA 3.0 |