Apologies in advance if any of my terminology here is wrong, I'm not an expert in statistics. If I've made any mistakes, let me know and I'll correct them.
The task I'm looking for some advice on approaching is parameterless density estimation (particularly kernel density estimation, but if somebody wants to suggest an entirely different approach I'd be interested in that too) in which there are many (100s or 1000s) of variables, but for each datapoint, I only know a small number of them (perhaps less than 100).
The known variables are not flatly distributed, and in fact the value of one variable (known or unknown) may have an effect on how likely another variable is to be observed. Whether or not a particular variable is observed may also have an effect on how likely another variable is to be observed.
Assume here that I have an extremely large number of datapoints. It should also be mentioned that the more often a variable, or combination of variables, is observed, the more important it is for me to be able to predict it. So, for example, if there's a certain value of variable X for which I never observe variable Y, I don't care about being able to estimate Y for that value of X.
Bandwidth selection in this situation is also something I could use some guidance on, for the kernel approach. I'd be happy to hear about either theoretical approaches or R packages.