Small area estimation of proportions with different levels of auxiliary data.

Binary data are often of interest in many small areas of applications. The use of standard small area estimation methods based on linear mixed models becomes problematic for such data. An empirical plug-in predictor (EPP) under a unit-level generalized linear mixed model with logit link function is often used for the estimation of a small area proportion. However, this EPP requires the availability of unit-level population information for auxiliary data that may not be always accessible. As a consequence, in many practical situations, this EPP approach cannot be applied. Based on the level of auxiliary information available, different small area predictors for estimation of proportions are proposed. Analytic and bootstrap approaches to estimating the mean squared error of the proposed small area predictors are also developed. Monte Carlo simulations based on both simulated and real data show that the proposed small area predictors work well for generating the small area estimates of proportions and represent a practical alternative to the above approach. The developed predictor is applied to generate estimates of the proportions of indebted farm households at district-level using debt investment survey data from India.

Localised estimates and spatial mapping of poverty incidence in the state of Bihar in India-An application of small area estimation techniques.

Poverty affects many people, but the ramifications and impacts affect all aspects of society. Information about the incidence of poverty is therefore an important parameter of the population for policy analysis and decision making. In order to provide specific, targeted solutions when addressing poverty disadvantage small area statistics are needed. Surveys are typically designed and planned to produce reliable estimates of population characteristics of interest mainly at higher geographic area such as national and state level. Sample sizes are usually not large enough to provide reliable estimates for disaggregated analysis. In many instances estimates are required for areas of the population for which the survey providing the data was unplanned. Then, for areas with small sample sizes, direct survey estimation of population characteristics based only on the data available from the particular area tends to be unreliable. This paper describes an application of small area estimation (SAE) approach to improve the precision of estimates of poverty incidence at district level in the State of Bihar in India by linking data from the Household Consumer Expenditure Survey 2011-12 of NSSO and the Population Census 2011. The results show that the district level estimates generated by SAE method are more precise and representative. In contrast, the direct survey estimates based on survey data alone are less stable.