A MODIFIED GENERALIZED ESTIMATOR FOR EFFICIENT POPULATION PARAMETER ESTIMATION IN TWO-PHASE STRATIFIED RANDOM SAMPLING

Abstract

Sampling is often conducted in multiple phases to optimize resources, reduce costs, and
improve accuracy. Two-phase sampling leverages on auxiliary information to enhance
efficiency. However, most existing estimators primarily focused on homogeneous populations.
Hence, leaving a gap in addressing heterogeneous populations. This study introduced a
modified generalized estimator within a stratified two-phase sampling framework, incorporated
auxiliary information at both sampling and estimation stages. The motivation behind this study
was to develop relatively more efficient estimators with reduced mean square error (MSE) for
heterogeneous populations. The objective was to derive and evaluate the performance of the
proposed estimators using real-life datasets and Monte Carlo simulations. Two real-life datasets
were utilized: the first dataset from the Joint Admissions and Matriculation Board (JAMB)
records on applicants by gender for 2017 and 2018, with 2018 serving as the variable of interest
and 2017 as the auxiliary variable. The second dataset consists of the enrolments of public
primary school pupils and number of teachers by gender and local government for the
2018/2019 academic session. The Taylor series expansion up to the second-degree
approximation was applied in deriving the MSE of the proposed estimators. The efficiency of
the estimators was assessed using real-life datasets and a Markov Chain Monte Carlo (MCMC)
simulation across varying sample sizes (5, 10, and 50). The result demonstrated decreasing
MSE values with increasing sample sizes and established that the proposed modified
generalized estimators effectively minimized MSE and maximized efficiency in two-phase
stratified random sampling as compared to the existing work proposed by Ashish et al (2023)
and the classical mean estimator under two-phase stratified sampling.