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I have $n$ observations of the following random variables: $$ Y+X_1,\ Y+X_2,...,\ Y+X_m,$$ where $${\bf E}X_1=\cdots= {\bf E}X_m=0.$$ The random variable $Y$ is independent of $X_1,...,X_m$. The random variables $X_1,...,X_m$ are dependent and differently distributed.

Is there a way to estimate the values of $X_1,...,X_m$ in the observations?

Viktor
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    If all the $ X $s have mean 0, presumably you only want to estimate their variance? If so, it sounds like you should look into regression with [heteroscadistic errors](https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors) as discussed [here](https://stats.stackexchange.com/questions/275925/linear-regression-with-changing-variance). – an1lam Feb 07 '20 at 13:27
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    **This cannot be solved** unless you can describe the nature of the dependency among the $X_i.$ For instance, if you can give their covariance matrix (up to some unknown constant multiple), this problem can be solved with weighted least squares. – whuber Feb 07 '20 at 16:48

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