A Study on the Variance of Estimators in Sampling with Varying Probabilities

Abstract

Under Sampling Theory, unequal probability sampling without replacement is the vital scheme to find the population parameters. Already various procedures are provided to find population parameters which are not providing complete satisfactory solution. Further, a large degree of emphasis has been laid in the literature on the use of auxiliary information towards improving the precision of estimates of the population parameters in finite populations. Auxiliary information is also being used for the purposes of stratification and for probability proportional to size sampling procedures. Hence, in this paper, an attempt is made for utilizing the auxiliary information to construct ratio estimator using Markov sampling for the population total and the efficiency of the estimator is compared with Horvitz-Thompson estimator towards finite population with linear trend. C programs have been written for this purpose and illustrations are provided.