In 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 it, but being an application journal they prefer a reference to a simple mathematical derivation.
Does anyone have any suggestions for a suitable reference? I thought there was something in Tukey's EDA book (1977) on sums and differences but I can't find it.