Timeline for Statistical models in terms of families of random variables
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2013 at 14:38 | comment | added | Tom LaGatta | The tricky part is regularity, then. This is the whole point of Kolmogorov's continuity theorem: the product construction does not guarantee regularity. I have to think about @John Dawkins' answer a little more. | |
| Nov 16, 2013 at 9:58 | comment | added | Adrien Hardy | I'm kind of lost: as Michael Greinecker recalled, you can always build a huge probability space in which all your variables live, whatever $\Theta$ is, thanks to the tensor product construction. Then, maybe the "natural" topology you look for just the convergence in distribution of random variables ? In this case, that $x:\Theta\rightarrow L$ is continuous is by definition equivalent to $P:\Theta\rightarrow \Delta(X)$ continuous. But maybe I misunderstood the question. | |
| Nov 16, 2013 at 8:51 | comment | added | Michael Greinecker | For the nontopological case, you can simply take $\Omega=X^\Theta$, $\mathcal{F}$ the product $\sigma$-algebry, $\mathbb{P}=\otimes_{\theta\in\Theta}P_\theta$ and $x_\theta$ the projection onto the $\theta$'s factor. | |
| Nov 16, 2013 at 2:46 | answer | added | John Dawkins | timeline score: 4 | |
| Nov 15, 2013 at 23:06 | history | asked | Tom LaGatta | CC BY-SA 3.0 |