Timeline for Are the coefficients of a linear combination of random vectors as random?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2016 at 13:25 | vote | accept | Rob | ||
| Mar 8, 2016 at 16:30 | answer | added | Robert Israel | timeline score: 2 | |
| Mar 8, 2016 at 13:01 | comment | added | Rob | @FedericoPoloni Yes! :-) | |
| Mar 8, 2016 at 12:43 | comment | added | Federico Poloni | @Rob Same comment: so, essentially, you want to find the distribution of the entries of $X^{-1}Y$? That is what the coefficients of that linear combinations are. | |
| Mar 8, 2016 at 12:27 | comment | added | Rob | @FedericoPoloni I changed the question so that it should be much clearer now what I would really like to know. | |
| Mar 8, 2016 at 12:24 | comment | added | Rob | @AnthonyQuas Thanks! I must confess my question was not very accurate. I changed it. In addition I specified the distribution as "absolutely". Is it actually the same as assuming $\mathbb{P}(X=x)=0$ $\forall x$ for the distribution? | |
| Mar 8, 2016 at 12:15 | history | edited | Rob | CC BY-SA 3.0 |
added "absolutely" and modified the question
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| Mar 7, 2016 at 18:59 | answer | added | Mark Fischler | timeline score: 0 | |
| Mar 7, 2016 at 18:29 | comment | added | Federico Poloni | So, essentially, find the distribution of $X^{-1}y$, where $X$ is obtained by stacking the $x_i$'s horizontally? | |
| Mar 7, 2016 at 18:00 | comment | added | Anthony Quas | Are you asking whether the random variables $(a_i)$ are iid? No definitely not (but they are exchangeable). Also, you said that every set of $n$ vectors from a continuous distribution is a.s. linearly independent. Is this a hypothesis? In general it's not true as the one-dimensional distribution along a line is continuous. (It is true if you say absolutely continuous distribution). To get a counter-example to your iid claim, you can consider distributions that are continuous, but a small perturbation of a discrete distribution. | |
| Mar 7, 2016 at 16:59 | history | asked | Rob | CC BY-SA 3.0 |