Timeline for If ϵ is uniformly distributed, then a linear probability model is appropriate? Can I find any Literature?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 12 at 13:52 | comment | added | optimal control | This is a very nice idea Alecos! | |
| Jun 11 at 17:18 | comment | added | Alecos Papadopoulos | @optimalcontrol Set $X^2 \equiv W$. If you can make the same underlying assumption about the distribution of $\epsilon | W$, i.e. $\epsilon\mid W\sim U(-a,a)$, then everything remains the same. At estimation time, $X$ is data so square it and use $X^2$ as your regressor. | |
| Jun 10 at 10:19 | comment | added | optimal control | Does the same result hold for a non-linear framework? Like if we have $X^2$ instead of $X$ ? | |
| Jan 7, 2023 at 13:58 | comment | added | Federico Tedeschi | I think the equation $$F_{\epsilon|X}(- b_0- b_1X\mid X) = \frac {- b_0- b_1X + a}{2a} $$ derives from $P[Z<k]=k$ for $Z\sim U(0,1)$, as made evident from your reply here: stats.stackexchange.com/a/105163/159259 . However, this only holds for $0 \leq k \leq 1$: for $k<0$, $P[Z<k]=0$, and, for $k>1$, $P[Z<k]=1$. Then, in case of out-of-range values, I’d say that such underlying latent variable foundation is in line performing OLS estimation first (given that the ML one wouldn't be feasible in such case) and then moving to 1 the values above 1, and moving to 0 negative values. | |
| Jan 10, 2014 at 11:15 | history | edited | Scortchi♦ | CC BY-SA 3.0 |
fixed typos
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| Jan 10, 2014 at 10:34 | history | answered | Alecos Papadopoulos | CC BY-SA 3.0 |