Spatiality in small area estimation: A new structure with a simulation study

In numerous practical applications, data from neighbouring small areas present spatial correlation. More recently, an extension of the Fay-Herriot model through the Simultaneously Auto- Rregressive (SAR) process has been considered. The Conditional Auto-Regressive (CAR) structure is also a popular choice. The reasons of using these structures are theoretical properties, computational advantages and relative ease of interpretation. However, the assumption of the non-singularity of matrix (Im-ρW) is a problem. We introduce here a novel structure of the covariance matrix when approaching spatiality in small area estimation (SAE) comparing that with the commonly used SAR process. As an example, we present synthetic data on grape production with spatial correlation for 274 municipalities in the region of Tuscany as base data simulating data at each area and comparing the results. The SAR process had the smallest Root Average Mean Square Error (RAMSE) for all conditions. The RAMSE also generally decreased with increasing sample size. In addition, the RAMSE valuess did not show a specific behaviour but only spatially correlation coefficient changes led to a stronger decrease of RAMSE values than the SAR model when our new structure was applied. The new approach presented here is more flexible than the SAR process without severe increasing RAMSE values.