Timeline for Linear model with hidden variable
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2016 at 17:03 | comment | added | Roland | Sorry, I'm not making myself clear. I certainly agree that it's impossible to estimate all parmeters a,b,c,d directly. I'm asking if there is anything known about estimation of the parameters that are uniquely obtainable. For example, if you have priors on b and d, how should we update them to a posterior given the data y, z. (I'm experimenting with this but wondering if anything similar has been done.) | |
| Dec 20, 2016 at 14:32 | comment | added | Radix | I don't think you can come up with a model for this. Let's say $b/d = \tau$ and $a - \tau \cdot c = \gamma$. The parameters $a$ and $c$ could be anywhere on the line $a - \tau \cdot c = \gamma$. Similarly, for $b$ and $d$, they can be anywhere on the line $b = \tau \cdot d$. Unless you have some additional information about at least one of these 4 parameters, all solutions are equiprobable. | |
| Dec 20, 2016 at 7:58 | comment | added | Roland | There is still some information about a,c in the problem -- essentially, the point estimate is a line in the (a,c) plane. The linear algebra is not hard, but the question is if this situation is understood as a statistical model. What parameterization is most tractable, are small sample distributions of estimators known, etc. | |
| Dec 19, 2016 at 17:56 | history | edited | Radix | CC BY-SA 3.0 |
originally missed the fact that the two equations are the same...
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| Dec 19, 2016 at 17:52 | comment | added | Radix | ah yes you are right, you can't find $a$ and $c$ because you essentially end up with two different representations of one equation, and the two unknown parameters $a$ and $c$. | |
| Dec 19, 2016 at 17:01 | comment | added | Roland | Yes, the quantities b/d and a - bc/d are easy to get. But that doesn't allow solving for a and c, as far as I can tell --- how would you do that? Fundamentally, only two independent parameters obtainable from a regression line, and a,c seem tangled up with the ratio b/d somehow. | |
| Dec 19, 2016 at 3:57 | review | First posts | |||
| Dec 19, 2016 at 6:48 | |||||
| Dec 19, 2016 at 3:54 | history | answered | Radix | CC BY-SA 3.0 |