I'm working with survey data and for $N$ larger domain units (in this case, spatial) I have an estimate of some response variable $y_i$ and covariate vector $x_i$ for $i\in \{1,...,N\}$. In each of these larger units, there are smaller units indexed $j=1,...,M_i$ which also have covariates $x_j$ but do not have the response variable $y_j$.
I'd like to generate a prediction $\hat{y}_j$ leveraging the correlation between $x$ and $y$. This problem appears to be closely related to that of area-level small area estimation, though this preprint states that going from coarse-to-fine resolution is generally a bad idea.
I've found it very challenging to find literature discussing the problem, though it seems to be one that comes up a fair amount in my data analysis. Are you aware of any resources on this? I've already spent a fair amount of time looking through the SAE literature including much of the work by JN Rao and the Fay-Herriott model.
