Timeline for How to prove that $X_1X_1', X_2X_2'$ are iid random matrices if we know that $X_1,X_2$ are iid random vectors?
Current License: CC BY-SA 4.0
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Oct 25, 2019 at 20:56 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 25, 2019 at 20:31 | comment | added | Learning math | thanks for pointing the reference out! | |
| Oct 25, 2019 at 20:14 | comment | added | Iosif Pinelis | Fact 1 corresponds to condition c) in Theorem 10.1 of Probability Essentials by Jacod and Protter, second ed., ISBN 3-540-43871-8. | |
| Oct 25, 2019 at 18:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 25, 2019 at 18:43 | comment | added | Iosif Pinelis | @Let'stalkmath : I think this can be found in some of the standard textbooks on probability theory. At this point, I don't have specific references to Facts 1 and 2 exactly. For me, such facts are much easier to prove than to find in the literature. Fact 1 can be proved a bit simpler, at least in the case when the measurable spaces are $\mathbb R^d$'s (as in your case), using a characterization of independence in terms of the expectation such as e.g. Lemma 6.12 in the text Probability by Davar Khoshnevisan. | |
| Oct 25, 2019 at 18:22 | comment | added | Learning math | Thank you for your answer, much appreciated. Could you recommend a textbok from where we could pikc up stuff like this? I know measure theory and part of measure-theoretic probability. | |
| Oct 25, 2019 at 18:22 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 25, 2019 at 18:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 25, 2019 at 18:04 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |