Small area estimation is any of several statistical techniques involving the estimation of parameters for small sub-populations, generally used when the sub-population of interest is included in a larger survey.
To deal with this problem, it may be possible to use additional data (such as census records) that exists for these small areas in order to obtain estimates.
The initial survey data, in which farmers reported the area they had growing either corn or soybeans, was compared to estimates obtained from satellite mapping of the farms.
is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage from the satellite data and
The Fay-Herriot model, a random effects model, has been used to make estimates for small domains when the sample from each domain is too small for fixed effects.