An Alternative Stratified Three-Stage Estimators for Finite Population Total

Abstract

This paper proposes two modified stratified three-stage estimators, denoted as 3M1 and 3M2, for estimating finite population totals under complex survey designs. The proposed estimators aim to improve efficiency by incorporating stratification and Probability Proportional to size (PPS) that reduce bias and variance. Their performance is assessed using both real-life and simulated data sets. Results demonstrate that 3M1 and 3M2 consistently achieve lower variance, mean squared error, and bias compared to conventional estimators such as Horvitz–Thompson (HT), Hansen–Hurwitz (HH), and Hájek Ratio (HR). Relative efficiency measures confirm substantial gains, with 3M1 performing optimally under Scenario 1 and 3M2 under Scenario 2. The study concludes that the proposed estimators provide reliable alternatives for national surveys and large-scale data collection involving stratified multistage designs with 3M1 preferred when balancing variance with bias is required and 3M2 when variance minimization is the priority.