On the calibration estimators of finite population proportion under remainder systematic sampling

Estimators of population parameters which utilized only information of the study variable tend to be sensitive to outliers or extreme values that may characterize sampling information due to randomness in selection thereby making them to be less efficient and robust. One of the approaches often adopted in sampling survey to address aforementioned issue is to utilize auxiliary variable information. Therefore, this study introduced a new calibration method for estimating a population proportion using remainder systematic sampling with the help of an auxiliary attribute. A new calibration scheme was developed and the theoretical expressions for the optimized resultant estimators for estimator proportion of population attribute were derived. The motivation for using calibration methods is due to their ability to reduce bias, enhance precision, utilize auxiliary information, provide flexibility, comply with standards, and improve decision-making. These benefits collectively contribute to more reliable and valid estimates, making them an essential aspect of modern sampling techniques. The theoretical findings were supported by simulation studies on nine populations generated using the binomial distribution with various success probabilities. The simulation results showed that the proposed estimators under the proposed calibration schemes performed more efficiently on average compared to the traditional unbiased estimator of the population proportion under remainder systematic sampling. The numerical results of the demonstrated the superiority of the proposed calibrated estimators over the existing conventional estimators in terms of biasness, efficiency, robustness, stability as well as efficiency gain.