| Summary: | 碩士 === 淡江大學 === 數學學系 === 92 === In survey sampling, sample mean is commonly used to construct confidence intervals of the finite population mean. However, when the finite population contains a large proportion of zeroes, the normal approximation may have very poor coverage rate even when the sample size is very large. Kvanli, Shen and Deng(1998) proposed a parametric likelihood approach to construct confidence intervals. They found that the new intervals have more precise coverage. If the finite population does not fit the assumed parametric model, their method may not work as nicely. So Chen, Chen and Rao(2003) used non-parametric method to develop empirical likelihood ratio intervals. However, when the finite population contains a large proportion of zeroes, we may have selected all zeroes in one sample. To avoid such situations, we find auxiliary information which have a correlation coefficient ρ with the target population. We first sort this auxiliary information from the smallest to the largest and divide them equally into four groups, then draw a sample according to the ratios of 10%, 20%, 30%, 40%. We use two different weights to calculate the likelihood functions and develop pseudo parametric and empirical likelihood ratio intervals. We discuss their relation ship with respect to correlation coefficient ρ and nonzero proportion p , and also analyze their lower and upper average bounds and coverage rates .
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