Timeline for Frisch-Waugh-Lovell theorem: How do we know this matrix is invertible?
Current License: CC BY-SA 4.0
7 events
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| Jan 14, 2023 at 14:33 | comment | added | Alecos Papadopoulos | @statmerkur Indeed, but it is needed in order for the reader to understand that invertibility of these two matrices goes together, so if we have a "regular" linear regression least-squares estimation, FWL is also available without further worries. | |
| Jan 13, 2023 at 8:49 | comment | added | statmerkur | +1 Though, I think there is no need to state that "and so $X′X$ is not invertible to begin with." since this was not used anywhere else in your proof. | |
| Jan 11, 2023 at 2:32 | comment | added | Alecos Papadopoulos | @statmerkur Thanks for the suggestion, I elaborated on it. | |
| Jan 11, 2023 at 2:31 | history | edited | Alecos Papadopoulos | CC BY-SA 4.0 |
Small correction responding to a comment
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| Jan 10, 2023 at 10:46 | comment | added | statmerkur | I think it should be "But in order to do so, this column vector must be in the column space of $X_1$" instead of "But in order to do so, this column vector must be inlcuded in the regressors used to form $P_1$". | |
| Mar 24, 2017 at 18:22 | comment | added | whuber♦ | +1 I believe you, because this theorem is an immediate consequence of an easily proven generalization to arbitrary partitions of the set of explanatory variables. (I describe this generalization geometrically at stats.stackexchange.com/a/113207/919 and algebraically, in terms that look similar to yours, at stats.stackexchange.com/a/46508/919.) | |
| Mar 24, 2017 at 17:14 | history | answered | Alecos Papadopoulos | CC BY-SA 3.0 |