Variance Estimation Using Quadratic Programming Technique
Authors: Raju Kumar*, Kaustav Aditya*, Hukum Chandra*, Pradeep Basak* and Shrila Das**
*ICAR-Indian Agricultural Stattistics Research Institute, New Delhi-12
** ICAR-Indian Agricultural Research Institute, New Delhi-12


The calibration approach is frequently used to develop estimators of various population parameters of interest and very frequently used by the statisticians for generation of official and Agricultural statistics in India because it gives precise estimates along with the Standard error which is needed for policy planning. The calibration approach involves deriving revised weights and using these weights in the form of a weighted estimator. The revised weights are developed by minimizing a distance function subject to the constraint that the weighted sample mean of auxiliary variables is equal to the population mean/total of the auxiliary variable. Generally, a chi-square type distance function is used for deriving revised weights. The approach is called as lower level calibration. A higher order calibration approach has been developed by Singh (1998) to improve the estimate of variance of the Horvitz-Thompson (1952) estimator. The higher level calibration approach makes use of known population variance of the auxiliary character. Many a times the chi-square type distance function gives negative weights. The negative weights when used in the variance estimator will give negative variance estimator. We use quadratic programming approach to obtain non-negative weights.

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About Author / Additional Info:
Working as a Scientist in the prestigious ICAR-Indian Agricultural Stattistics 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