Analysis of unit level models for small area estimation in crop statistics assisted with satellite auxiliary information

Crop statistics for a small area, such as the community development block, are an increasingly important topic in agricultural statistics. Under normality assumptions, the classic Empirical Best Linear Unbiased Prediction (EBLUP) technique is effective for predicting small area means, however the Small Area Estimation (SAE) model can be heavily affected by the incidence of outliers or deviations from the expected distribution. The purpose of this study was to estimate variance, predict block-level wheat crop yield in the Hisar and Sirsa district of Haryana by classical SAE method and a robust random-effect predictor using a slight generalization of Huber’s Proposal 2. In the case of Sirsa district, the results of classical and robust unit level SAE were very close, but not in the case of Hisar district. This could be due to the influential observation found in the Hisar data set. More accurate EBLUP wheat yield estimates are obtained when the Huber-type M-estimation method is initialized by the least square regression estimator.