Data imputation for statistical analysis Here is the situation:
I have an individual level data set $X$ where each row is a person $i$ and each column denote characteristics of $i$. The problem is that my data is missing an important variable, lets call this $z_{i}$. 
To resolve this situation I am considering using data imputation. Note, I have not done this before so I am: (a) a bit unsure of how it actually works in practice, (b) when it can be considered a valid thing to do (and when it is not appropriate). Information pertaining to each of these, or both would therefore be valuable. 
My perception of the approach, and proposed way of proceeding is the following (please let me know if this is wrong):
I do not have data on $z$ in my dataset, but I have access to other data from which I could devise a empirical CDF $F(z)$. Next I would simply draw from this distribution and crudely impute these data into a new column in my dataset $X$. Is this the general approach taken? 
I understand that a more appropriate approach would be to devise the conditional empirical cdf $G(z|X’)$ and to sample form this. I can actually do that because I have a separate sample where a proxy for $z$ is available--call it $z'$, so I could probably use this to get $G(z'|X)$. Would I next simply draw from these conditional distributions in order to construct the new imputed variable in the old dataset $X$?
I understand that these questions are rather naive, and I understand that any procedure of this kind must come with its own set of assumptions that will restrict when it is and is not appropriate, but the suggestions above are simply my take on the "intuition" behind the approach, and I firstly want to make sure that this is correct. Second, any information pertaining to the assumptions required on the data would be much appreciated too.
 A: If your other data and your new data set X are both random samples from the same underlying population and both have data on the same variables (except for variable z in set X), then you could combine all the data and perform multiple imputation to estimate the missing data in set X. You might also be able to include your separate sample with values for the proxy z' if that data set also has values on the other variables.
As you recognize in your description of the "more appropriate approach," treating z as independent of the other variables is not appropriate; you need to consider its multivariate relations to the other variables. Multiple estimates based on the multivariate empirical distribution and pooling of analyses among the imputations is crucial.
There are several approaches; the website http://www.stefvanbuuren.nl/mi/MI.html has a brief overview, with links to more detailed descriptions and to software packages that implement them.
If, however, your new data set X is not really comparable to your other data sets, then you really shouldn't combine the data sets in this way and I don't know of a reliable way to impute the missing data.
