| Summary: | 碩士 === 淡江大學 === 數學學系 === 89 === In survey sampling, sample mean is commonly used to construct confidence intervals of the finite population mean. However, the precision of the normal approximation depends on the skewness of the population. When the finite population contains a large proportion of zeroes, the normal approximation can be very poor even when the sample size is very large. Kvanli, Shen and Deng (1998) proposed a parametric likelihood approach to construct the confidence interval. They found that the new intervals have more precise coverages in many situations. A key contribution of their method is to select the appropriate parametric models that fit the finite population under investigation. If the parametric model does not fit to the finite population, their method may not work as nicely. A natural remedy is to use non-parametric method. Empirical likelihood methodology has been recently proposed by Owen (1988, 1990, 1991), Chen and Qin (1993), and Qin and Lawless (1994). It does not rely on parametric model assumptions imposed on the data set. In addition, a related likelihood ratio statistics has the usual chi-square limiting distribution under very minor moment assumptions. Extensive simulation studies indicate that the empirical likelihood method and the parametric likelihood approach proposed by Kvanli et al (1998) both have the same precise coverage rate. Thus, the empirical likelihood is idea method being used in the situation when a model is not desirable, and the population contains a large proportion of zeroes.
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