MODIFIED DIFFERENCE-CUM DUAL TO EXPONENTIAL TYPE
ESTIMATOR OF THE POPULATION MEAN UNDER NON-RESPONSE
Mukesh Kumar, Pooja Yadav
1Associate Professor, Department of Statistics, University of Lucknow, Lucknow-226007, India *Email:mukesh.stat@gmail.com; 2Research Scholar, Department of Statistics, University of Lucknow,Lucknow-226007, India, Email:yadavpooja3831@gmail.com
Abstract
Survey sampling is almost essential for the study of large populations. The estimators of population parameters such as population total, mean, variance, etc., are proposed to obtain the best estimate of say, GDP, income, commodities, etc. on various occasions. The auxiliary information is frequently used to get the best estimate. Further, in most of the sample surveys, many targeted and required responses are generally not received due to various reasons. Statistically, it is termed a non-response problem and without proper handling of this issue, might produce incorrect estimates and results. Therefore, a technique proposed by Hansen and Hurwitz (1946) is used to deal with the problem of non-response. In this technique, the targeted units considered into two groups one as a response group and the other as a non-response group. Further, a sub-sample from the non-response group was contacted, again to obtain the response. Both the sample responses and subsample responses were collectively used for estimation, which produced quite satisfactory results. In this research, we have proposed a generalized estimator of population mean for the variable under study with the use of auxiliary variables in the presence of non-response. The bias and mean squared error (MSE) expressions for the proposed estimator have been obtained considering the first order of approximation. The MSE of the suggested estimator has been compared with the MSE of similar existing estimators theoretically and empirically. For, empirical findings, percent relative efficiency (PRE), has been reported and higher PRE means a more efficient estimator. The proposed estimator is shown to be generalized and performs better in terms of efficiency than most of the existing estimators and hence suitable for many reallife applications
Keywords: Auxiliary information, Bias, MSE, PRE, Exponential estimator, non-response error.
