Timeline for What happens in the martingale CLT if I norm by the conditional variance instead?
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Nov 9, 2018 at 19:03 | history | bounty ended | CommunityBot | ||
| S Nov 9, 2018 at 19:03 | history | notice removed | CommunityBot | ||
| Nov 3, 2018 at 19:58 | comment | added | Taro Tokyo | Then, to me, the 'dependence' mecanism is not truly clear. Would you mind restating in terms of $\theta,X,Y,n_i$ ? | |
| Nov 3, 2018 at 19:53 | comment | added | Taro Tokyo | Not really. If your target stream data has temporal structures, for example, derivative prices, precipitation, etc, there are plenty of possible complementary hypothesis we have to clarify. And as you are looking for a theoretical result, it is essential to be clear. Nevertheless, that was to be sure. | |
| Nov 3, 2018 at 19:15 | comment | added | gogurt | @TaroNGUYEN Yes, that is precisely what is meant. I didn't think it was too ambiguous to be honest, but I'm always happy with edits for clarity. | |
| Nov 3, 2018 at 17:15 | comment | added | Taro Tokyo | ... Let $(n_i)_{i \ge 1} $ be an array of positive real numbers. Define $S_k = \sum_{i=1}^k n_i$ ; $\hat{\theta}_i= \frac{1}{n_i} \left( \sum_{m= S_{i-1}+1}^{S_i} X_m-Y_m\right)$ " ? | |
| Nov 3, 2018 at 17:13 | comment | added | Taro Tokyo | In first 2 papagraphs, do you want to say ? " Given 2 arrays of random variables $(X_n)$ and $(Y_n)$ such that i) $(X_n)$ are idd, (Y_n) are idd ii) $(X_n) \perp \!\!\! \perp (Y_n)$ iii) $X_1$ and $Y_1$ are square integrable. | |
| Nov 3, 2018 at 17:07 | comment | added | Taro Tokyo | In my opinion, we should put more work on the statement of your problem. At this point, it is still unclear. | |
| Nov 3, 2018 at 16:34 | history | edited | gogurt | CC BY-SA 4.0 |
Rephrased question to ask about norming by conditional variance.
|
| Nov 2, 2018 at 2:38 | history | edited | gogurt | CC BY-SA 4.0 |
Rearranged expression to make explicit that the desired norming is the variance of $T_{n,k}$.
|
| Nov 1, 2018 at 21:37 | history | edited | gogurt | CC BY-SA 4.0 |
added 312 characters in body
|
| S Nov 1, 2018 at 17:17 | history | bounty started | gogurt | ||
| S Nov 1, 2018 at 17:17 | history | notice added | gogurt | Draw attention | |
| Nov 1, 2018 at 14:41 | history | edited | gogurt | CC BY-SA 4.0 |
Adding an idea for how to approach this.
|
| Oct 31, 2018 at 13:35 | review | Close votes | |||
| Nov 1, 2018 at 17:20 | |||||
| Oct 31, 2018 at 13:11 | history | edited | gogurt | CC BY-SA 4.0 |
Grammar, spelling, succintness
|
| Oct 30, 2018 at 18:09 | history | edited | gogurt | CC BY-SA 4.0 |
Clarification on dependence of $p_i$ on $\hat{\theta}_{i-1}$
|
| Oct 30, 2018 at 18:08 | comment | added | gogurt | @MarcusM Can we start by making no assumptions on this dependence and see if we can get something out of that? | |
| Oct 30, 2018 at 17:36 | comment | added | Marcus M | How does $p_i$ depend on $\hat{\theta}_{i-1}$? | |
| Oct 30, 2018 at 17:15 | review | First posts | |||
| Oct 30, 2018 at 17:16 | |||||
| Oct 30, 2018 at 17:11 | history | asked | gogurt | CC BY-SA 4.0 |