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I am reading lecture note (Stanford stat361: https://web.stanford.edu/~swager/stats361.pdf) written by Stefan Wager. At page 23-24 the author states dependent summands become independent after conditioning. Is there someone can explain this formally? In addition, the conditional variance used here also seems weird.

By the way, this note is great since there is only few systematic introduction about the causality. However, it is not rigorous enough with respect to math language. Can someone recommend some other references?

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  • $\begingroup$ Have you seen Miguel Hernan and James Robins's free textbook on causal inference? It may not be as technical as you'd like, but it's still a good reference. hsph.harvard.edu/miguel-hernan/causal-inference-book $\endgroup$
    – RobertF
    Commented Oct 31, 2021 at 20:49
  • $\begingroup$ Yes, I have. It's comprehensive in the sense of introduction, but less helpful when tackling technical points like asymptotic behaviors. $\endgroup$
    – Ivan.lee
    Commented Nov 2, 2021 at 2:39

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