Timeline for Test whether expected shortfalls of two distributions are equal
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2021 at 5:23 | comment | added | Richard Hardy | Meaningful in what sense? If I have two identical data generating processes, chances are they will not generate the same sample of data sample with the same ES (or different samples with the same ES). | |
| Oct 26, 2021 at 3:31 | comment | added | user225256 | If the distribution is truly fixed, then I think any difference is meaningful. | |
| Oct 20, 2021 at 18:16 | comment | added | Richard Hardy | Unlike the more complicated question in the linked thread, here I assume a fixed distribution for all of the 1000 data points. So I guess there is no jumpy process, just 1000 i.i.d. observations. | |
| Oct 20, 2021 at 17:57 | comment | added | user225256 | What can you assume about the distribution of the data? If you generate it using a jumpy process, then the numerical instability in calculated VaRs and expected shortfalls probably makes the whole question intractable. | |
| Oct 20, 2021 at 17:20 | comment | added | Richard Hardy | I simulated the difference between a pair of ES values each estimated from a sample from the same $N(0,1)$ distribution. The distribution I got is indeed roughly normal. Anyway, I am not really comfortable with an assumption of bivariate normality (or lognormality) for the data. | |
| Oct 20, 2021 at 16:57 | comment | added | user225256 | My intuition is that the difference between two similar distributions should be roughly normal, which is why I said that this a reasonable first null hypothesis, but I don't have a formal argument for it. If the normality is a big concern you can generate lots of $M,N,R,S,T$ from the distributions and just see where $f(M_0,N_0,S_0,T_0)$ fits in the quantiles for $f(M,N,S,T)$. | |
| Oct 20, 2021 at 16:41 | comment | added | Richard Hardy | What is the intuition (or formal argument) for $f$ being roughly normal? | |
| Oct 20, 2021 at 16:11 | history | answered | user225256 | CC BY-SA 4.0 |