Timeline for How to check numerically iterated logarithm law ? (How to choose cutOff lim_n sup_{m: n<= m<= CutOff} ) ?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2016 at 9:14 | comment | added | Basj | @AlexanderChervov I have the same problem here math.stackexchange.com/questions/1637989/… and here math.stackexchange.com/questions/1637233/… and | |
| Feb 3, 2016 at 17:16 | comment | added | Alexander Chervov | @IosifPinelis Thank you for your comments. Still I am curious can one numerically test LIL ? | |
| Feb 3, 2016 at 15:33 | comment | added | Iosif Pinelis | (III) Also, real data distributions usually have much heavier tails than normal (because heavy tails are preserved by mixing and convolution). It is natural to expect that heavier tails will need lower cutoffs; cf. e.g. arxiv.org/abs/math/0610519. | |
| Feb 3, 2016 at 15:08 | comment | added | Iosif Pinelis | Continued: (I)(iii) Because of the possible high sensitivity to the independence, the quality of the pseudorandom number generator may be very important. Do you know if it has been tested for the LIL? (II) Anyhow, I think that insight into the magnitude of the appropriate cutoff could be gained by following the lines of the proof of the LIL. | |
| Feb 3, 2016 at 15:08 | comment | added | Iosif Pinelis | (I) I don't think that in most cases the law of the iterated logarithm (LIL) is the best tool to analyze real data (even really big data). (I)(i) For one thing, the factor $b_n:=\sqrt{\ln\ln n}$ grows very slowly. E.g., to get $b_n>2$, you need $n>5\times10^{23}$, almost as large as the Avogadro number; for $b_n>3$, you need $n>10^{3519}$ (the number of the elementary particles in the observale universe is about $10^{80}$, if I recall correctly). (I)(ii). The LIL should be very sensitive to the i.i.d. assumption, especially its independence part. | |
| Feb 3, 2016 at 10:03 | history | asked | Alexander Chervov | CC BY-SA 3.0 |