Abstract
The present investigation deals with the problem of estimation of population median in presence of non-response under two-phase (double) sampling. Using information on two auxiliary variables, four general classes of estimators have been suggested for four different realistic situations of non – responses. It is shown that several estimators can be generated from our proposed classes of estimators. Proposed classes of estimators are compared with some contemporary estimators of population median under the similar realistic situations. The merits of the proposed strategies have been interpreted through empirical studies carried over three natural populations and one artificially generated population data sets. This establishes effectiveness of the suggested classes of estimators. Suitable recommendations to the survey statistician have been made.
Highlights
In survey sampling, statisticians often come across the study of variables which have highly skewed distributions, such as income, expenditure etc
Kuk and Mak (1989) are the first to introduce the estimation of population median of the study variable using auxiliary information in survey sampling
Efficiency Comparisons of the Classes of Estimators T1 and T2 When non-response situations is observed on the study variable y as well as on the auxiliary variable x in the second phase sample of size n, we compare the efficiencies of our proposed classes of estimators Ti (i = 1, 2) under their respective optimality conditions with the estimators M *y, t*i (i = 1, 2) and present them below. (a) Efficiency Comparisons of the class of estimators T1 : It could be concluded from equations (33) and (37) - (39) that
Summary
Statisticians often come across the study of variables which have highly skewed distributions, such as income, expenditure etc. Situation III: In this case, we assume that the non-response situation occurs only on the study variable y while the complete information on the auxiliary variable x is available in second phase sample of size n and the population median Mz of the second auxiliary variable z be known Considering this situation, we have proposed the general class of estimators of population median My in two-phase sampling as. Situation IV: In this case, we assume that at the second phase sample non-response situation is found on the study variable y and the auxiliary variable z with unknown population mean Mz while the complete information about the auxiliary variable x is available there Considering this situation, we have suggested the general class of estimators of population median My in two-phase sampling as. Proceeding as above, it can be found that the classes of estimators T3 and T4 are very wide and the following estimators can be identified as their member
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