Impact of Varying Sampling Fraction on Relative Bias of the Linear Weighted Estimators to the First and Second Degree of Approximations in Unequal Probability Sampling

In this paper we have studied the role of varying sampling fractions on relative bias of conventional ratio estimator and also for the linear combination of ratio and PPS estimators to the first and second degree of approximations for a wide variety of populations. It will give the survey practitioners an idea whether it is worthwhile to ignore the expressions of mean sum of squares to the order O(n). A well known Quenoullie [1] method of splitting the sample into two random sub samples of equal size is used to define linear weighted estimator with approximately zero bias, to the first order of approximations. The summary statistics for the percentage absolute bias of conventional ratio estimator and that of linear combination of ratio and PPS estimators are also given.