Class of Calibrated Estimators of Population Proportion Under Diagonal Systematic Sampling Scheme

Ahmed Audu (), Maggie Aphane, Jabir Ahmad and Ran Vijay Kumar Singh
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Ahmed Audu: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa
Maggie Aphane: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa
Jabir Ahmad: Department of Statistics, Usmanu Danfodiyo University, Sokoto 840101, Nigeria
Ran Vijay Kumar Singh: Department of Mathematics, Kebbi State University of Science and Technology, Aliero 840101, Nigeria

Mathematics, 2024, vol. 12, issue 24, 1-15

Abstract: Estimators of population characteristics which only exploit information of the study characters tend to be prone 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 surveys to address the aforementioned issue is to incorporate supplementary character information into the estimators through a calibration approach. Therefore, this study introduced two novel methods for estimating population proportion using diagonal systematic sampling with the help of an auxiliary variable. We developed two new calibration schemes and analyzed the theoretical properties (biases and mean squared errors) of the estimators up to the second-degree approximation. The theoretical findings were supported by simulation studies on five populations generated using the binomial distribution with various success probabilities. Biases, mean square errors (MSE) and the percentage relative efficiency (PRE) were computed, and the results revealed that the proposed estimators have the least biases, the least MSEs and higher PREs, indicating the superiority of the proposed estimators over the existing conventional estimator. The simulation results showed that our proposed estimators under the proposed calibration schemes performed more efficiently on average compared to the traditional unbiased estimator proposed for population proportion under diagonal systematic sampling. The superiority of the results of the proposed method over the conventional method in terms of bias, efficiency, efficiency gain, robustness and stability imply that the calibration approach developed in the study proved to be effective.

Keywords: calibration; diagonal systematic sampling; auxiliary character; outliers; precision (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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