General Estimation Procedures of Population Mean in Two-Occasion Successive Sampling under Random Non-response
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RESEARCH ARTICLE
General Estimation Procedures of Population Mean in Two-Occasion Successive Sampling under Random Non-response Mohd Khalid1 • G. N. Singh2
Received: 26 June 2018 / Revised: 23 June 2020 / Accepted: 26 August 2020 The National Academy of Sciences, India 2020
Abstract In this paper, an attempt has been made to minimize the negative impact of random non-response in the estimation of population mean on current occasion in two-occasion successive sampling. A general class of estimators has been proposed, and their properties are studied under the assumptions that the number of sampling unit on which information may not be obtained follows a discrete probability distribution due to random non-response behavior. Properties of the proposed class of estimators are also derived for as individual cases when random non-response occurs either on the first or the second occasion. Empirical study has been carried out to show the efficacious performances of the proposed class of estimators over an estimator defined for the complete response situations. Suitable recommendations have been made to the applied survey practitioners for their real-life practical applications. Keywords Successive sampling Random non-response Auxiliary variable Bias Mean square error Mathematics Subject Classification 62D05
1 Introduction In a sample survey, successive (rotation) sampling is the useful and efficient survey methodology for producing the reasonably good estimates of the desired parameters when & Mohd Khalid [email protected] 1
Aligarh Muslim University Aligrah, Aligarh 202002, India
2
IIT(Indian School of Mines), Dhanbad 826004, India
the population characteristics are more likely to change with the time. The theory of successive sampling was first examined by Jessen [1], who considered the problem of estimation for population mean on current occasion by utilizing the information which already collected on the previous occasion. Patterson [2] and Tikkiwal [3] have made detailed study of successive sampling and have extended Jensen’s results to more than two occasions. Sen [4–6] has proposed this theory on two occasions in the presence of multi-auxiliary information when all the auxiliary variables are positively correlated with the study variable y; values taken by one of the auxiliary variables may be the values of y on the previous occasion. Further, Chaturvadi and Tripathi [7], Bridar and Singh [8], Singh and Priyanka [9], Singh and Viswakarma [10] and Singh et al. [11], among others, proposed estimation procedures of current population mean on two-occasion successive sampling where they made the use of auxiliary information on both the occasions. All the works which are mentioned above focused only on the estimation of populations mean when the complete responses were observed in survey data. In this paper, an effort has been made to estimate the population mean under the situations when sample data are missing due to random non-response. There are so many practical situations where the enti
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