Timeline for Predict lower and upper bounds for some total value
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2018 at 12:38 | vote | accept | Bas van der Reijden | ||
| Mar 27, 2018 at 7:16 | comment | added | Federico Tedeschi | If the conditions of my edit of 25/03/18 are met, then you have that the $Y_i$ are jointly independent, thus their covariances are all zero's. Under the same conditions, their variance is given by $\beta^2*SE^2(X_i)+SE^2(\epsilon_i)$. The variance of $Y$ is then given by $\sum_{i=1}^{n}a_i^2*SE^2(Y_i)$. In case the Lindeberg condition is satisfied (I think possible questions on it are more fit on the Math forum), you can then apply the $CLT$, eventually deriving your CI for $Y$ from its (approximate) normality. | |
| Mar 26, 2018 at 17:17 | comment | added | Bas van der Reijden | Thanks, I now think we come to the point and I can do something with this result! To summarize: I'll have to make estimates of the variances of $Y_i$, calculate the covariance matrix of $Y_1...Y_n$ (which is zero I suppose, because of the independence in observations?), consequently add the variances of $Y_i$ to obtain the variance of $Y$ and apply the CLT in order to make a prediction interval for $Y$? | |
| Mar 26, 2018 at 6:57 | comment | added | Federico Tedeschi | I edited my reply again. I assumed you asked about the covariance matrix of the set of $2n$ variables $X_1,\ldots, X_n, Y_1,\ldots, Y_n$: did I understand correctly? | |
| Mar 25, 2018 at 16:26 | history | edited | Federico Tedeschi | CC BY-SA 3.0 |
added 975 characters in body
|
| Mar 25, 2018 at 14:02 | comment | added | Bas van der Reijden | Response on the edited version: The variables $Y_i$ are predictions made on the properties of (independent) $X_i$'s; furthermore n exceeds 10.000. I (can correctly?) assume that $Y_i$ are independent and hence I think I'll use the (modified version such as Lindeberg or Lyaponuv, which does not assume that the $Y_i$'s are ident. distributed) CLT to let $Y$ be normally distributed ;)! Lastly, I was questioning myself if it is possible to use the modified CLT for sums of random variables and if I can calculate the cov matrix by using info about the $X_i$ and $Y_i$? | |
| Mar 24, 2018 at 22:08 | history | edited | Federico Tedeschi | CC BY-SA 3.0 |
added 1137 characters in body
|
| Mar 23, 2018 at 19:01 | comment | added | Bas van der Reijden | Thank you for your Response! In fact I was targeting at the sum of the quantiles of some prediction interval. But, as far as I can understand, it's not possible to 'add the quantiles' of $a_i y_i$ to construct a prediction interval for $y=\sum^n_i a_ i y_i$ and I have to do something with the individual standard deviations.. Do you have any suggestions how i can construct a prediction interval for $y$ in case I do not certainly know whether $y_i$ and the corresponding $y$ are normal but I do know each $\sigma_(y_i)$ the corresponding $\sigma_y$?? | |
| Mar 20, 2018 at 15:04 | history | answered | Federico Tedeschi | CC BY-SA 3.0 |