Timeline for Unbiased least squares estimate for GM Theorem
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2022 at 14:01 | comment | added | Richard Hardy | @akiro, you are welcome! | |
| Jan 18, 2022 at 12:56 | vote | accept | Dime | ||
| Jan 18, 2022 at 12:56 | comment | added | Dime | Much clearer now, thank you! | |
| Jan 18, 2022 at 11:51 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| Jan 18, 2022 at 11:25 | comment | added | Richard Hardy | @akiro, we never replace $Y$ with $\hat Y$. $Y=X\theta+\varepsilon$ per definition of $\theta$ and $\varepsilon$, while $\hat Y=X\theta$. It is not $Y$ that comes from an OLS estimate, because $Y$ is the actual data. The only thing related to $Y$ that comes from OLS is the fitted values $\hat Y$. | |
| Jan 18, 2022 at 9:28 | comment | added | Dime | Im not sure to understand your answer as it doesn't seems to answer my original question. Taking $\hat{Y} = X\theta$ or $\hat{Y} = X\theta + \epsilon$ is not really the part that bothers me. In fact I really don't understand how, conceptually, we can replace $Y$ with $\hat{Y}$ in the $\stackrel{\ast}{=}$ step. For me, $Y$ comes from the OLS estimate closed formula (and in a real world problem is the provided data labels) whether $\hat{Y}$ is the model prediction itself (which is conceptually different from the ground truth). | |
| Jan 17, 2022 at 15:18 | vote | accept | Dime | ||
| Jan 18, 2022 at 9:21 | |||||
| Jan 6, 2022 at 16:50 | history | answered | Richard Hardy | CC BY-SA 4.0 |