U. C. SudROHAN KUMAR RAMAN2017-06-142017-06-142014http://krishikosh.egranth.ac.in/handle/1/5810020021t-9052The mail questionnaire method is commonly used to collect data in surveys as the data collection costs following this method are considerably reduced. However, non-response can be serious problem in this method of data collection. The presence of non-response may result in biased estimates, particularly, when the respondents differ from the nonrespondents. Hansen and Hurwitz (1946) proposed a technique for adjusting nonresponse to obtain unbiased estimator. The calibration technique, proposed by Deville and Särndal (1992), is widely used to obtain precise estimators of population parameters. The technique provides a systematic approach for incorporation of auxiliary information at the estimation stage. Calibration implies that a set of starting weights (usually the sampling design weights) are transformed into a set of new weights, called calibrated weights. In this research work, estimators for population total have been proposed using the Hansen and Hurwitz (1946) technique through the calibration approach, described in Deville and Särndal (1992) and Särndal (2007), for different situations. Expressions for variance and estimator of variance, to the first order of approximation, of proposed calibrated estimators in presence of non-response have also been developed. The performance of developed calibrated estimators is evaluated through a simulation study where the study population is generated through an assumed model and also by making use of real data. Using the calibration approach, the Hansen and Hurwitz (1946) technique based estimator is developed for the situation where the information on auxiliary variable is assumed known for the entire sampled units and the proposed calibrated estimators outperforms the Hansen and Hurwitz estimators in terms of efficiency. Further, calibration approach based estimators using multiple sets of weights in the context of non response are considered. As expected, in terms of criterion of percent relative biases, the calibrated estimator based on known auxiliary information dominates the other estimators i.e., Hansen and Hurwitz estimator, Cochran ratio B B estimator (Cochran (1977)) and double sampling ratio estimator (Okafor and Lee, 2000)). It is observed that for situations involving positive correlation between known auxiliary variable and the study variable, the proposed calibrated estimator out performs in terms of criterion of relative root mean square error the Hansen and Hurwitz estimator, Cochran ratio estimator and double sampling ratio estimator. The double sampling approach based calibrated estimator is developed when auxiliary information is unknown. Simulation results clearly reveal that maximum improved performance occurs for large sample size as well as for high correlation between study and auxiliary variable. When information on a known auxiliary variable is negatively correlated with the study variable, it is observed that the proposed calibrated product estimator has consistently smaller values of the percent relative root mean square error as compared to the Hansen and Hurwitz estimator, Hansen and Hurwitz approach based Cochran product estimator and corresponding double sampling approach based product estimator. However, if auxiliary information is not available for entire population, the double sampling approach based calibrated product estimator is preferable. It is worthwhile to mention that the results based on simulations involving real data are similar to the case when simulations are performed involving population generated through an assumed model.en-USnullThesis