| Summary: | 博士 === 淡江大學 === 管理科學學系 === 89 === In finite population sample surveys, it is conventional to estimate the ratio of two population means by the ratio of corresponding sample means. A number of variations of ratio estimators have been proposed, whereas most of them are in single version but not in general form. We, therefore, intend to investigate for constructing almost unbiased estimators of finite population mean by suitably combining a set of transformed estimators. We also study the performance property up to the second degree of approximation. Moreover, an empirical study is carried out in order to understand better the performance of the new estimator compared to some commonly used estimators.
The use of auxiliary information in estimation of population parameters is usually assumed that all the observations on selected units in the sample are available. However, in many practical situations, some observations may be missing instead of all the observations are available. Incomplete information is common in practice and the traditional estimating procedures cannot be applied in this circumstance. We then investigate the ratio estimation for the situation that there is some incomplete information on study and auxiliary variables separately. The discussion includes the cases while the population mean of auxiliary variable is known or not. Further, we also considered a distribution of random incompleteness, which leads the estimation strategies to be available in practical application. The above discussions may be regard as an extension of the general consequences.
Finally, a slight modification of linear systematic sampling procedure that maintains the simplicity of selection is proposed. The procedure depends on the remainder only and can be used for population size being not a multiple of sample size. This procedure will be named as remainder linear systematic sampling. As the remainder is zero, the suggested method reduces to the usual linear systematic sampling procedure. One may view the remainder linear systematic sampling as an extension of linear systematic sampling. Moreover, we also compare the efficiency of the proposed sampling scheme with some other sampling schemes for various types of populations.
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