Jiming Jiang

Title

Developing a practical measure for small area estimation

Abstract

The mean squared prediction error (MSPE) is widely used in small area estimation (SAE). Despite its popularity, the MSPE is not always practical in that it treats positive error, or over-prediction, and negative error, or under-prediction, equally. In practice, however, the consequences of these two types of errors are often different. A closely related object is the so-called best predictor (BP), which is equal to the conditional expectation under the MSPE criterion. We develop an asymmetric MSPE (AMSPE) measure that assigns different weights to the two different types of prediction errors. It is shown that, under the normality assumption, the AMSPE-based BP has a simple and elegant expression. As a natural measure of uncertainty, a second-order unbiased estimator of the area-specific AMSPE of the empirical BP is also developed. The developments are detailed under the area-level model. Theoretical properties of the proposed EBP and its AMSPE estimator are studied and their empirical performances are evaluated. An iterative procedure for determining the weight in the AMSPE is developed and its convergence property is established. A real-data example is discussed.

Keywords

• Empirical best predictor
• Measure of uncertainty
• Small area estimation