Application of Calibration Approach for Regression Coefficient Estimation under Two-stage Sampling Design
Authors: Pradip Basak, Kaustav Aditya, Hukum Chandra and U.C. Sud
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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1. Introduction
Now a days, survey data are complex and multivariate in nature which involves clustering, stratification, unequal probability of selection, multi-stages and multi-phases. The traditional method of estimation of regression coefficient is ordinary lest squares (OLS) estimation which is based on the assumption that sample observations are drawn independently. This assumption of independence holds only if the sample observations are drawn using simple random sampling with replacement (SRSWR) but for other sampling designs it does not hold. One such complex design is two-stage sampling design which is widely used in large scale surveys. In two-stage sampling, sample is selected in two stages. In the first stage, clusters are selected and in the second stage, a specified number of elements are investigated from the selected clusters. The clusters which form the units of sampling at the first stage are known as primary stage units (PSU) and the elements within the clusters are known as second stage units (SSU). As for example, in case of crop, surveying fields can be taken as first stage units and plots within the fields can be taken as second stage units.

Kish and Frankel (1974) suggested use of sampling design weights in the estimation procedure as an alternative to the OLS. Estimation of regression coefficient based on maximum likelihood estimation was suggested by Holt, Smith and Winter (1980).In the presence of auxiliary information, calibration approach was suggested by Deville and Sarndal, 1992 for the improvement of the estimator of population parameters. Work on calibration approach based estimation of population parameters like mean, total, proportion, covariance has already been done under uni-stage or multi-stage designs, see for example Aditya et al. (2016), Plikusas and Pumputis (2007, 2010).Thus, under the availability of auxiliary information in the two-stage design, the theory of calibration approach is used here for the improvement of the estimator of population regression coefficient.

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About Author / Additional Info:
Working as a Scientist in the prestigious ICAR-Indian Agricultural Statistics Research Institute, New Delhi-12 and published many research articles in national and international journals. Currently working in the field of estimation of crop area and production in India and other methodological issues like small area estimation, domain estimation, GPS, survey methodology and official statistics