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I came across the following example from a book. I am given a dataset generated from a bivariate normal distribution:

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Among the data, there are missing values for the last 20 of x2i (but not for x1i). The example demonstrates how EM algorithm comes into play to impute the missing value. The procedures are attached below:

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It is further commented that the E-step conditional expectation is derived from the following formula:

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I don't understand how this formula (the one with epsilon) is derived. Could anyone give me a reference for that?

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marked as duplicate by whuber Dec 13 '18 at 17:30

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ The quotation is puzzling because you show us equation $(4.1)$ but the explanation refers to equation $(4.3)$ which isn't shown. To give you a useful answer, we need definitions of all variables and all distributional assumptions that are being made. $\endgroup$ – whuber Dec 13 '18 at 17:10
  • $\begingroup$ Thanks for pointing it out. I have supplemented the post with more information. See if it is sufficient $\endgroup$ – yalex314 Dec 13 '18 at 17:20
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    $\begingroup$ Thank you: your question is clearer now. I believe you can it answered in very many ways on our site: check out stats.stackexchange.com/…. I'm pretty sure I answered it at stats.stackexchange.com/a/71303/919, for instance, using elementary geometry, but of course there are many other ways to approach this. $\endgroup$ – whuber Dec 13 '18 at 17:28