Abstract
In this paper, possible solutions of problem of non-response in the variable of interest are proposed when information about an auxiliary attribute is available. By taking motivation from the previous work, modified classes have been suggested for estimating population mean. Two new generalized classes of estimators are presented along with their asymptotic biases and variances. Efficacy analysis of the suggested classes is acquired with the usual regression estimator. Two real examples have been provided to show the efficiency of the proposed design approach and comparison of suggested estimators with the linear regression estimator.
Highlights
Introduction and literature reviewIn sample surveys while estimating an unknown population parameter of the study variable, use of the auxiliary information increases the efficiency of the estimates
Suggested classes we have introduced two general classes of estimators for the population mean assuming non-response occurs in the study variable with known information on the auxiliary attribute
Three modified classes of estimators motivated by Shabbir and Gupta (2007), Koyuncu (2012) and Singh and Solanki (2012) have been considered in presence of non-response
Summary
Modified classes we have considered Shabbir and Gupta (2007), Koyuncu (2012) and Singh and Solanki (2012) classes because those are more efficient than the regression estimator. Shabbir and Gupta (2007) suggested a class of ratio estimator for the population mean Yusing known information of the auxiliary attribute. Later Singh and Solanki (2012) and Koyuncu (2012) proposed classes on the same subject using different known population parameters such as (ρpb, Cp) etc. First modified class Shabbir and Gupta (2007) proposed the class of estimators ySG = yw1 + w2(P − P ). If we assume that there is non-response on Y, the class (6) can be modified as y∗M1 = y∗ w1 + w2(P − P ). We can modify the class (12), assuming non-response on Y y∗M2 = w1y∗ + w2(P − P ).
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