Efficient estimation method of population mean with non-response and observational error under ORRT models

This study addresses the difficulties faced by surveyors in collecting responses to sensitive questions, which lead to non-sampling errors such as non-response and observational error. To tackle these issues, we employ optional randomized response technique (ORRT) models under simple random sampling and two-phase sampling. A new class of estimators are introduced to simultaneously account for social desirability bias, non-response and observational error. These estimators are evaluated against existing methods to assess their properties and effectiveness. The proposed approach leverages ORRT models to estimate the population mean of a sensitive study variable. To validate the theoretical findings, an empirical study is conducted using simulation models for both sampling scenarios separately. The simulation results demonstrate the effectiveness of the proposed class of estimator.