Ratio-product cum regression variance estimators in the presence of random Nonresponse

Abstract

The variability of a population under study can be estimated using variance estimators so that better policies can be devised. This study aimed to propose a new approach for estimating the variance of a finite population using auxiliary information, while accounting for two common scenarios of random non-response in simple random sampling is suggested. The proposed estimator was derived using linear combination approach. The power series and exponential series were used in deriving the properties of the estimator (bias and mean square error). The properties were compared theoretically with existing estimators, up to the first level of approximation. The theoretical conditions for efficiency under the two scenarios of random non-response were established. The criteria of mean square error and percentage relative efficiency were used in assessing the performance of the estimator. The empirical findings using real datasets revealed that the proposed estimators performed better than the existing variance estimators with minimum mean square error and higher percentage relative efficiency values.  Thus, the proposed estimator can be utilized to estimate population variability in real-world scenarios where random non-response occurs.