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12:51 PM
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Q: Reference for the sum and difference of highly correlated variables being almost uncorrelated

Rob HyndmanIn a paper I've written I model the random variables $X+Y$ and $X-Y$ rather than $X$ and $Y$ to effectively remove the problems that arise when $X$ and $Y$ are highly correlated and have equal variance (as they are in my application). The referees want me to give a reference. I could easily prove...

This question is arguably a duplicate of this more recent question
5
Q: What is the intuition behind the independence of $X_2-X_1$ and $X_1+X_2$, $X_i \sim N(0,1)$?

JohnKI was hoping someone could propose an argument explaining why the random variables $Y_1=X_2-X_1$ and $Y_2=X_1+X_2$, $X_i$ having the standard normal distribution, are statistically independent. The proof for that fact follows easily from the MGF technique, yet I find it extremely counter-intui...

The latter question has received a few more detailed answers, but IMO Dmitrij Celov's comment to Rob's question is what immediately springs to my mind. Whether it is intuitive or not I don't know.
 
 
1 hour later…
1:58 PM
@AndyW, so you're wondering if you should vote to close the older Q? I would put a comment w/ a link on both, but not vote to close. Rob's Q asks for a reference & the new Q asks for the intuition, so they may be just far enough apart.
 

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