Abstract
The present investigation deals with the problem of estimation of population mean in presence of non-response under two-phase (double) sampling. Following the technique of sub-sampling of non-responding group adopted by Hansen and Hurwitz (1946) and using information on two auxiliary variables, four general classes of estimators have been suggested for four different situations of non-response and their properties are studied. It is shown that several estimators can be generated from our proposed classes of estimators. Comparisons of the proposed strategies with some contemporary estimators of population mean in presence of non-response are carried out. The results obtained are illustrated numerically through empirical studies which present the effectiveness of the suggested classes of estimators. Sri Lankan Journal of Applied Statistics 2015;16(1):41-68
Highlights
In surveys covering human populations in most cases, information is not obtained from all the units in the survey at the first attempt even after some call-backs
It is well known fact that in sample surveys precision in estimating the population mean may be increased by using information on single or multiple auxiliary variables
Motivated by the above suggestions and following the two-phase sampling structure defined above with the assumption that the population mean of the auxiliary variable x be unknown, we have proposed following four general classes of estimators of population mean Y of the study variable y applicable for four different situations of non-response
Summary
In surveys covering human populations in most cases, information is not obtained from all the units in the survey at the first attempt even after some call-backs. With Y, X, X, Z and G y*, x, x , z satisfies the similar regularity conditions given for Y, X, X, Z and F y*, x*, x , z in equation (9) In this case, we assume that in the second phase sample non- response situation is found on the study variable y and the auxiliary variable z with unknown Z while the complete information on the auxiliary variable x is available. We assume that in the second phase sample non- response situation is found on the study variable y and the auxiliary variable z with unknown Z while the complete information on the auxiliary variable x is available Considering this situation, we have suggested the general class of estimators of population mean.
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