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This paper considers the problem of estimation of the population total under probability proportional to size (PPS) sampling scheme when complete data is not available due to the presence of missing observations or non-response. The suggested estimators are developed based on available multi-auxiliary information for the response group and non-response group utilizing the calibration approach. The variances of the suggested estimators have been derived up to the first order of approximation. A simulation study done on a real dataset using R software also supports the performance of the suggested estimators. The empirical percentage absolute relative biases (%ARB) and percentage relative root mean squared errors (%RRMSE) are computed for the suggested estimators. The developed estimators are compared with the estimators of the population total due to the design-based Horvitz and Thompson (HT) estimator and calibration HT type estimator obtained on the available complete response units along with the design-based Hansen and Hurwitz (HH) estimator in the presence of non-response.
Garg et al. (Sat,) studied this question.