On indirect estimation of small area parameters under ranked set sampling

Abstract

In investigations of domains under post-stratified random sampling, it is difficult to get an acceptable precision for domain-specific estimates due to low sample sizes. Small area estimate, a popular technique that has been widely used over the past few decades, involves indirect estimating using the auxiliary data from the entire population. In this article, we utilize a ranked set sampling (RSS) technique to achieve a greater level of precision in area-specific estimations under the assumption that ranking the smaller sets is simple, inexpensive, and flawless. RSS optimizes sample size for a fixed degree of precision or increases precision for a fixed sample size. We create direct estimators for population total under homogeneous, ratio, and regression models that are area specific. To evaluate the effectiveness and application of the suggested RSS technique, data from the Pakistan Demographic Health Survey (PDHS 2017–18) and Iris flower data are used. The effectiveness of the RSS mechanism is supported by both theoretical characteristics and Bootstrapped tests.

Keywords

• Precision
• Sub-population estimation
• Auxiliary data
• Sample size