On the modified regression-cum-ratio type estimators of population variance in the presence of non-response and measurement error

Abstract

This study proposes three classes of modified regression-cum-ratio type estimators of the finite population variance under simple random sampling when both the study and auxiliary variables are affected by non-response and measurement errors. Each estimator combines a regression component with a dual-to-ratio, exponential, or ratio-exponential product transformation based on known auxiliary parameters. First-order expressions for the bias and mean squared error (MSE) were derived, together with conditions under which the proposed estimators are more efficient than existing ones. Performance was evaluated by Monte Carlo simulation on five artificial populations (N = 1,000, n = 100, 1,000 samples), with measurement error added to both variables. Using bias, MSE, and percentage relative efficiency (PRE), the estimators were compared with the sample variance estimator and the estimators of Isaki, Singh et al., Yadav and Kadilar, Asghar et al., and Audu et al. All proposed estimators had smaller MSEs than the sample variance estimator in every population. The exponential-type estimators Υ22 and Υ23 outperformed all existing estimators in every population, with Υ22 attaining PREs of about 11,025%, 9,276%, 20,834%, 1,264%, and 20,833% in Populations I to V, respectively. The ratio-exponential product-type estimators were less efficient than some Audu et al. estimators in Populations II, III, and V. Biases of the proposed estimators were small, except in Population IV, where all estimators were markedly biased. The proposed estimators are therefore efficient alternatives for variance estimation under non-response and measurement error.