Timeline for Convergence of estimator given by a fixed point
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2020 at 20:17 | vote | accept | T. Tharoor | ||
| Mar 12, 2020 at 19:53 | comment | added | Iosif Pinelis | I have added a proof of the almost sure convergence. | |
| Mar 12, 2020 at 19:52 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 803 characters in body
|
| Mar 12, 2020 at 16:43 | comment | added | T. Tharoor | From the strong law of large numbers, for all $s$ $H_t(s)\to H_\infty(s)$ almost surely. But from there I do not see how to pursue. | |
| Mar 12, 2020 at 15:19 | vote | accept | T. Tharoor | ||
| Mar 12, 2020 at 19:04 | |||||
| Mar 12, 2020 at 12:58 | comment | added | Iosif Pinelis | @pyth : (i) It is significantly easier to get almost sure convergence (by using the strong law of large numbers) than the rate of convergence (for which you need a central limit theorem, and then the rate can be only given for the convergence in distribution). I decided to focus on the harder part of the problem. (ii) (1) is not a simple central limit theorem: we need uniformity in $s$, which is not provided by the standard central limit theorem. | |
| Mar 12, 2020 at 8:06 | comment | added | T. Tharoor | Moreover, as far as I understand, $(1)$ is the central limit theorem, why do you need a stronger result? | |
| Mar 12, 2020 at 7:40 | comment | added | T. Tharoor | Thank you for your answer. Correct me if I'm wrong but this does not imply almost sure convergence, right? | |
| Mar 11, 2020 at 16:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 24 characters in body
|
| Mar 11, 2020 at 15:42 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |