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Nonparametric moment estimation with an index function

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george pepper
george pepper 2020-2-13
Hello,
I try to estimate the mean of the random variable t conditional on t being in a certain category, denoted S_j. The expected value of t also depends on an observable index value, denoted x. How can I compute the expected value of t for a given x and a given category S_j? Mathematically, I try to compute:

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