In this paper, we have developed estimators of finite population mean using Mixture Regression estimators using multi-auxiliary variables and attributes in two-phase sampling and investigated its finite sample properties in full, partial and no information cases. An empirical study using natural data is given to compare the performance of the proposed estimators with the existing estimators that utilizes either auxiliary variables or attributes or both for finite population mean. The Mixture Regression estimators in full information case using multiple auxiliary variables and attributes are more efficient than mean per unit, Regression estimator using one auxiliary variable or attribute, Regression estimator using multiple auxiliary variable or attributes and Mixture Regression estimators in both partial and no information case in two-phase sampling. A Mixture Regression estimator in partial information case is more efficient than Mixture Regression estimators in no information case.

Abstract:It is a common experience in sample survey that data cannot always be collected for all units selected in the sample at the first attempt and even after some call-backs. An estimate obtained from such incomplete data may be misleading because of the non-response in the data. In addition, the population mean of the auxiliary variable from the previous census may not be available. In this paper, Modified regression type estimators proposed by Tum et al. (2014) in single phase sampling, assuming complete response, have been proposed to estimate the population mean of the study variable in the presence of non-response under two phase sampling scheme. The expression of mean squared errors (MSE) based on the proposed estimators have been derived under two phase sampling to the first degree of approximation. A comparison of the proposed estimators with the usual unbiased estimator and existing estimators under two phase sampling scheme have been carried out. The proposed Modified regression type estimators have been found to be the most efficient compared to the existing estimators and they are recommended for use in practice.