The use of satellite data and survey data to estimate crop and livestock production at county level is becoming popular. Although there are several models for doing prediction, these models are not robust to model failure. These data are not usually normally distributed and a transformation is usually necessary to have an approximate fit of a model. Given data, which may not be normally distributed, from a number of similar areas (e.g., counties), we use a rank-based method to estimate the finite population mean of one of these areas. We use the nested error regression model, which permits "borrowing of strength" from other areas. One important feature of our method is that there is no need to assess the assumption of normality necessary to implement most methods for small areas, and another feature is that we do not require a transformation. We use R-estimates of the model parameters to construct a predictor of the population mean of a small area, and the mean squared error of the predictor is also obtained. Finally, we illustrate the methodology using the well-known satellite and survey data obtained from 12 counties in north-central Iowa (U.S.) to assess the acreage cultivated with corn and soybean.

Key Words
Asymptotic; Crop production; Dispersion function; Mean squared error; Nested error model; Residual; R-predictor.

M. Mushfiqur Rashid is Mathematical Statistician, Division of Biometrics III, HFD 720, Center for Drug Evaluation and Research Food and Drug Administration, 5600 Fishers Lane, Rockville, MD 20857. Balgobin Nandram is Associate Professor, Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609.