~ 1360 ~ International Journal of Chemical Studies 2020; 8(5): 1360-1371 P-ISSN: 2349–8528 E-ISSN: 2321–4902 www.chemijournal.com IJCS 2020; 8(5): 1360-1371 © 2020 IJCS Received: 25-06-2020 Accepted: 06-08-2020 Ajay Kumar Gautam Department of Agricultural Statistics, Acharya Narendra Deva University of Agriculture and Technology, Ayodhya, Uttar Pradesh, India Manoj Kumar Sharma Department of Statistics, Mathematics and Computer Science, SKN College of Agriculture, Sri Karan Narendra Agriculture University, Jobner, Jaipur, Rajasthan, India BVS Sisodia Department of Agricultural Statistics, Acharya Narendra Deva University of Agriculture and Technology, Ayodhya, Uttar Pradesh, India Corresponding Author: Manoj Kumar Sharma Department of Statistics, Mathematics and Computer Science, SKN College of Agriculture, Sri Karan Narendra Agriculture University, Jobner, Jaipur, Rajasthan, India Development of calibration estimator of population mean under non-response Ajay Kumar Gautam, Manoj Kumar Sharma and BVS Sisodia DOI: https://doi.org/10.22271/chemi.2020.v8.i5s.10491 Abstract Using the calibration approach, the Hanson and Hurwitz (1946) technique-based estimator is developed for the situation where the information on auxiliary variable is assumed known for the entire sample units. Expressions for the estimator of population mean/total, its variance, and variance estimator were developed. The theoretical results are illustrated with the help of empirical studies. Empirical results showed that proposed calibration approach-based estimator outperforms the Hansen and Hurwitz technique. Keywords: Calibration approach, Hansen and Hurwitz estimator, non-response, population mean Introduction In many human surveys, it generally is not possible to obtain information from all the units in the surveyed population. The problem of non-response persists even after call backs. The estimates obtained from incomplete data may be biased particularly when the respondents differ from the non-respondents. To address the problem of bias, Hansen and Hurwitz (1946) [2] proposed a technique essentially to adjust for non-response. The technique consists of selecting a sample from the population, identifying the non-respondents in the sample and selecting a sub sample of non-respondent. When the auxiliary information on auxiliary variable related to study variate in available, Deville and Särndal (1992) have developed calibration approach based estimator of the finite population mean/total of the study variate by calibrating sampling design weight using certain calibration equation which involve known population mean/total of the Auxiliary variable. Methods of estimation of finite population mean under non-response in sample surveys using auxiliary information have been developed by various research workers in the past which have been explained in the previous chapter. Raman et al. (2013 a, 2013 b) have developed calibration estimator of the finite population total under non-response depending upon the different situation of availability of the auxiliary information. However, before we present a brief account of their work, we will first describe the Hansen and Hurwitz (1946) [2] estimator under general sampling design. It may be mentioned that the weighting and imputation procedures aim at elimination of bias caused by non-response. However, these procedures are based on certain assumptions on the response mechanism. When these assumptions do not hold good the resulting estimate may be seriously biased. Further, when the non-response is confounded, i.e. the response probability is dependent on the survey character. It becomes difficult to eliminate the bias entirely. Theoretical developments Consider that the finite population U=(1,2,….k,…,N) consists of N identifiable sampling units. Consider that a sample sa of size na is drawn by sampling design P(.) from U with first and second order inclusion probabilities πak and πakl, l K  .we also define =  akl πakl-πakπal , U l k   …(1.1)