Eblup Estimates by Using Remotely Sensed Data

The knowledge of auxiliary variables for entire population is a necessary task in many agricultural applications; for example a method widely applied to improve the efficiency of crop area estimations is the regression estimator (Cochran, 1977), that exploit the correlation between classified satellite images (auxiliary information) and ground surveys’ data. The regression analysis offer a lot of advantages, even if it’s highly affected by two main problems: the presence of outliers which usually implies instability in the regression parameters estimates and the so called scale problem (MAUP) that is the use of aggregated data increase artificially the amount of correlation between variables (Openshaw e Taylor, 1979). According to the aforesaid problems and considering that generally the final goal is to obtain crop area estimations at small area level (usually districts/provinces), the idea is to improve the direct estimator using small area models that relate the small area surface to area specific auxiliary variables, instead of using regression analysis on the sampled point (which generally represent a very small portion of the territory). Generally the linking models based on random area-effects that account for between area variations other than the variation explained by auxiliary variables are called small area models and the indirect estimator based on small area models will be called “model-based estimators”. The aim of this work is to produce area estimates of the main crops at a provincial, regional and national level, using as sampling design a stratified two-phase sampling. We improve the direct Horwitz-Thompson estimator whit the two stage model of Fay and Herriot (1979) and the EBLUP (Empirical Best Linear Unbiased Predictors) estimators (Rao, 2003). A spatial autocorrelation amongst the small area units has been also considered to improve the small area efficiency. Spatial models are a special case of a mixed linear model and therefore EBLUP estimator con be easily obtained. Moreover, we have valuated the importance of good auxiliary data for the success of model-based methods. In fact, cloudy whether is usually the main source of missing data in satellite images. All the missing data and outliers (considered as missing) have been imputed, whit a technique called Multiple Imputation (MI Rubin, 1987). In the MI instead of imputing a single value for each missing value, m value are drawn from the predictive distribution and then complete data analysis is repeated a given number of times, say h. ) / ( obs miss Y Y P We confirmed that the combination of small area model whit the technique of spatial autocorrelation and Multiple Imputation improve the crop area estimations compared with direct estimations. To illustrate the proposed approach, we applied the spatial EBLUP estimation and the MI method for missing covariates to the AGRIT 2005 data.