Penalized Chi Square Distance Function in Survey Sampling

In the present investigation, we propose a penalized chi square distance function for estimating the total/mean of a finite population. The function produces a general class of estimators for the population total that includes, among others, the estimators of Searls (1964), Singh and Srivastava (1980), and the famous unbiased ratio estimator of Hartley and Ross (1954). Several of the estimators in the resulting general class are not members of the family based on the pioneer technique of Deville and Sarndal (1992). The existing gap in the GES developed at Statistics Canada to study Searls’ (1964) estimator and unbiased estimation through calibration could be filled with the help of technology developed here.