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Not AvailableImproved chain-ratio estimators for the population mean based on two-phase sampling are proposed when the study variable and two auxiliary variables comprise non-response. Auxiliary information is available for the first variable and not available for the second variable. Their biases and mean square errors are estimated under large sample approximation. Their efficiencies are compared with Hansen and Hurwitz’s estimator, the ratio and regression estimators for a single auxiliary variable, and Singh and Kumar’s estimators for two auxiliary variables. Empirical evaluations using both model-based and design-based simulations show that these estimators perform better than Hansen and Hurwitz’s estimator, the ratio and the regression estimators, and Singh and Kumar’s estimator.Not Availabl