摘要：The generalised mixed ratio-cum-product estimators in Two-phase sampling has been developed and recommended using multi-auxiliary variables for Full Information Case (FIC), Partial Information Case I (PIC-I) and No Information Case (NIC) estimators. However, the PIC-I estimators would not obey the conditions of usage if both the ratio and product estimator components were not in partial information case, simultaneously. Hence, this study has considered two additional PIC (PIC-II and PIC-III) estimators which satisfied two more conditions for any PIC estimator in the family mixed estimator. Theoretical comparison established that the proposed PIC-II and PIC-III estimators were asymptotically efficient than PIC-I estimator. Similarly, the empirical analysis and comparison for thirty three simulated populations, following normal distribution, confirmed the asymptotic efficiency of the proposed estimators. The proposed estimators were recommended not as substitute but as complimentary estimators to the PIC-I estimator, subject to the confirmation of the conditions of usage. Special case estimators were developed based on the settings of the unknown constants in the proposed estimators.
关键词：Ratio-cum-product estimator;Multi-auxiliary variables;Two-phase sampling;Partial information case.
