Enhanced Robust Estimators for Population Mean Accounting for Non-Response and Measurement Error

Abstract

Estimators play a crucial role in statistics, quality assurance, and survey methodology, which estimate key population characteristics like: the mean, variance, and standard deviation based on sample values. However, data collection in medical and social sciences often faces significant challenges due to non-response and measurement errors, which complicate the data compilation, computation, and estimation processes. This study proposes a robust class of estimators that address these challenges by incorporating call-back and imputation schemes and parameters accounting for measurement errors, thereby enhancing estimator efficiency despite the adverse effects of non-response and measurement errors. The properties of these proposed estimators, including bias and mean square errors (MSEs), were derived using a second-degree Taylor series approximation, and a consistency test was performed. The research also established the conditions under which the proposed estimators are more efficient than existing ones. An empirical study utilizing simulated data from distributions—normal, exponential, chi-square, uniform, gamma, and Poisson—demonstrated that the modified estimators under the imputation scheme are significantly more efficient and reliable than the existing alternatives. Consequently, these modified classes of estimators are recommended for practical application, particularly in scenarios involving non-response and measurement errors during data analysis and estimation.

Estimators play a crucial role in statistics, quality assurance, and survey methodology, which estimate key population characteristics like: the mean, variance, and standard deviation based on sample values. However, data collection in medical and social sciences often faces significant challenges due to non-response and measurement errors, which complicate the data compilation, computation, and estimation processes. This study proposes a robust class of estimators that address these challenges by incorporating call-back and imputation schemes and parameters accounting for measurement errors, thereby enhancing estimator efficiency despite the adverse effects of non-response and measurement errors. The properties of these proposed estimators, including bias and mean square errors (MSEs), were derived using a second-degree Taylor series approximation, and a consistency test was performed. The research also established the conditions under which the proposed estimators are more efficient than existing ones. An empirical study utilizing simulated data from distributions—normal, exponential, chi-square, uniform, gamma, and Poisson—demonstrated that the modified estimators under the imputation scheme are significantly more efficient and reliable than the existing alternatives. Consequently, these modified classes of estimators are recommended for practical application, particularly in scenarios involving non-response and measurement errors during data analysis and estimation.