Finite Population Mean Estimation through a Two-Parameter Ratio Estimator Using Auxiliary Information in Presence of Non-Response

Abstract

In surveys covering human populations it is observed that information in most cases are not obtained at the first attempt even after some callbacks. Such problems come under the category of non-response. Surveys suffer with non-response in various ways. It depends on the nature of required information, either surveys is concerned with general or sensitive issues of a society. Hansen and Hurwitz (1946) have considered the problem of non-response while estimating the population mean by taking a subsample from the non-respondent group with the help of extra efforts and an estimator was suggested by combining the information available from the response and nonresponse groups. We also mention that in survey sampling auxiliary information is commonly used to improve the performance of an estimator of a quantity of interest. For estimating the population mean using auxiliary information in presence of nonresponse has been discussed by various authors. In this paper, we have developed estimators for estimating the population mean of the variable under interest when there is non-response error in the study as well as in the auxiliary variable. We have studied properties of the suggested estimators under large sample approximation. Comparison of the suggested estimators with usual unbiased estimator reported by Hansen and Hurwitz (1946) and the ratio estimator due to Rao (1986) have been made. The results obtained are illustrated with aid of an empirical study.

Promoting Statistical Practice and Collaboration in Developing Countries

“…Sampling experts further exploited that idea and used auxiliary information to improve the precision of nonresponse estimators. Many researchers have expanded the idea and proposed different estimators when nonresponse is expected for both study variable and auxiliary variables or for either, like Cochran (1977), Rao (1986), Khare and Srivastava (1993, 1997, Singh and Kumar (2008), Sing et al (2009), Kumar and Bhougal (2011), Singh et al (2009), Chanu and Singh (2015), Pal and Singh (2016), and Zubair et al (2018).…”

A New Family of Exponential Type Estimators in the Presence of Non-Response

“…After the significant contributions of these studies, Yunusa and Kumar [17], Dansawad [18], Singh and Usman [19], Pal and Singh [20,21], Yadav et al [22], Sinha and Kumar [23], Pal and Singh [24], Kumar and Kumar [25], Sanaullah et al [26] and Javaid et al [27] have proposed exponential type estimators for the population mean for Case I.…”

Exponential Type Estimators Using Sub-Sampling Method With Applications in Agriculture

“…Using the sub-sampling method, Rao (1986) proposed the classical ratio   adapting the estimator proposed by Bahl and Tuteja (1991) to the Case I. Following these estimators, Olufadi and Kumar (2014), Yadav et al (2016), Kumar and Kumar (2017), Pal and Singh (2016, 2018, Dansawad (2019), Usman (2019a, 2019b), Unal and Kadilar (2021) proposed various estimators taking the advantage of the exponential function.…”

“…Under the Case II, Cochran (1977) defined the ratio   2 R t and regression   2 reg t estimators while Singh et al (2009) proposed the exponential type estimator for the population mean. Following these estimators, Kumar and Bhougal (2011), Kumar (2013), Yadav et al (2016), Kumar and Kumar (2017), Pal and Singh (2016, 2018, Usman (2019a, 2019b), Kadilar (2020, 2021) and Riaz et al (2020) proposed estimators using the exponential function for the population mean for the Case II.…”