Timeline for Conditional Expectation of Multivariate Distributions
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2017 at 13:47 | history | edited | kjetil b halvorsen♦ |
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| Oct 5, 2012 at 15:07 | vote | accept | CommunityBot | ||
| Oct 5, 2012 at 15:04 | comment | added | user8968 | My book states (as a particular case) : E[X] = E[E[X|Y]]. My book is Craig and Hogg 7th edition. | |
| Oct 5, 2012 at 9:42 | comment | added | Xi'an | I do not know what is "intuitive" and what is not "intuitive", but this result is a version of the double projection theorem, namely that the orthogonal projection (on $A$) of the orthogonal projection (on $B$ with $A\subset B$) is the orthogonal projection (on $A$). | |
| Oct 5, 2012 at 4:10 | answer | added | Zen | timeline score: 11 | |
| Oct 5, 2012 at 3:00 | history | edited | Michael R. Chernick | CC BY-SA 3.0 |
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| Oct 5, 2012 at 1:07 | comment | added | whuber♦ | Inquest, I don't think @Zen intended to sound threatening with that question. I take it as an abbreviated way of asking, "what is your understanding of the meaning of $\mathbf{E}[X_2|X_2]$?". Your clarification of this will establish a starting point for answers that address your intuition and what you would like to see as a proof. | |
| Oct 4, 2012 at 23:53 | history | undeleted | user12451 | ||
| Oct 4, 2012 at 23:53 | history | deleted | user12451 | ||
| Oct 4, 2012 at 23:42 | comment | added | Zen | Do you understand what $\mathrm{E}[X_2\mid X_1]$ is? | |
| Oct 4, 2012 at 23:40 | history | edited | Zen | CC BY-SA 3.0 |
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| Oct 4, 2012 at 23:31 | comment | added | cardinal | What you've written is not true, perhaps simply due to a typo (the RHS is missing an expectation operator). The (correct) result follows almost immediately from the definition of conditional expectation. Could you please cite your source explicitly and edit your post to provide the result actually stated in the book? | |
| Oct 4, 2012 at 23:28 | comment | added | kjetil b halvorsen♦ | ¿Maybe you should give the name of the textbook? Why is the result intuitive: Consider you have an $N\times M$ matrix and want the mean of the components. You can compute it in three ways: directly, the mean of all the components. Or first the mean of all the rows, and then the mean of the rowmeans. Or you can do the same with row replaced by column. All this give clearly the same answer. The stated theorem is just a theoretical version of this result. | |
| Oct 4, 2012 at 23:15 | history | asked | user8968 | CC BY-SA 3.0 |