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In this article, we will construct an alternative Hartley-Ross unbiased ratio estimator for the population mean of a study variable when related auxiliary information is available. We will also present some efficiency comparisons and related results and give a numerical illustration.

In this paper we have examined certain techiques suggested in the literature for improving the ratio and regression methods of estimation and demonstrated that these techniques are not very profitable.

Using the criterion of minimum expected variance and the Horvitz-Thompson estimator, we study various πPS (πi, the probability of inclusion of the ith unit, Proportional to Size) strategies and make a comparison between these strategies under a general super population model. This discussion further motivates the search for a class of designs which are best suited for the use of the Horvitz-Thompson estimator. A new class of such designs is obtained.