Small Area Shrinkage Estimation

Abstract

The need for small area estimates is increasingly felt in both the public and private sectors in order to formulate their strategic plans. It is now widely recognized that direct small area survey estimates are highly unreliable owing to large standard errors and coefficients of variation. The reason behind this is that a survey is usually designed to achieve a specified level of accuracy at a higher level of geography than that of small areas. Lack of additional resources makes it almost imperative to use the same data to produce small area estimates. For example, if a survey is designed to estimate per capita income for a state, the same survey data need to be used to produce similar estimates for counties, subcounties and census divisions within that state. Thus, by necessity, small area estimation needs explicit, or at least implicit, use of models to link these areas. Improved small area estimates are found by “borrowing strength” from similar neighboring areas.

The key to small area estimation is shrinkage of direct estimates toward some regression estimates obtained by using in addition administrative records and other available sources of information. These shrinkage estimates can often be motivated from both a Bayesian and a frequentist point of view, and indeed in this particular context, it is possible to obtain at least an operational synthesis between the two paradigms. Thus, on one hand, while small area estimates can be developed using a hierarchical Bayesian or an empirical Bayesian approach, similar estimates are also found using the theory of best linear unbiased prediction (BLUP) or empirical best linear unbiased prediction (EBLUP).

The present article discusses primarily normal theory-based small area estimation techniques, and attempts a synthesis between both the Bayesian and the frequentist points of view. The results are mostly discussed for random effects models and their hierarchical Bayesian counterparts. A few miscellaneous remarks are made at the end describing the current research for more complex models including some nonnormal ones. Also provided are some pointers for future research.