A class of estimators in two-phase sampling with subsampling the non-respondents

Motivated by Singh and Kumar [14], we introduce in this paper a general class of estimators for the population mean of a study variable when two auxiliary variables are used in the presence of non-response. The minimum asymptotic variance bound of the estimators belonging to the class is determined and the optimality of Singh-Kumar estimators discussed. The best estimator in the class is analytically found in accordance with the auxiliary information used and the efficiency gain that can be achieved upon competitive estimators is shown by an empirical study.