Abstract
In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.
Highlights
One of the common problems in sample surveys is non-response
We propose two new families of estimators for estimating the cumulative distribution function (CDF) using information on the sample distribution function, mean and ranks of the auxiliary variable along with the information on the sample distribution function of the study variable under simple random sampling in the presence of non-response
High non-response rates create opportunity or risk for bias in estimates and affect survey design, data collection, estimation and analysis Plewes et al [27]. With these issues in mind, we propose two new families of estimators for estimating the CDF using information on the sample distribution function, mean and ranks of the auxiliary variable along with the information on the sample distribution function of the study variable under simple random sampling in the presence of non-response
Summary
One of the common problems in sample surveys is non-response. The non-response bias is serious concern in survey studies. We propose two new families of estimators for estimating the CDF using information on the sample distribution function, mean and ranks of the auxiliary variable along with the information on the sample distribution function of the study variable under simple random sampling in the presence of non-response. High non-response rates create opportunity or risk for bias in estimates and affect survey design, data collection, estimation and analysis Plewes et al [27] With these issues in mind, we propose two new families of estimators for estimating the CDF using information on the sample distribution function, mean and ranks of the auxiliary variable along with the information on the sample distribution function of the study variable under simple random sampling in the presence of non-response.
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