一般在分析抽樣資料時, 通常是使用傳統的常態近似法。但當資料含有大量零值時, 傳統方法會變得不可靠。利用Kvanli et al (1998) 所提出的最大概度比法處理多零值資料會比傳統方法準確。本文利用 Chen 和 Sitter (1999) 提出將傳統概度函數加權所發展出的擬概度函數, 再結合 Cochran (1977) 的不等機率抽取法來處理具輔助訊息的多零值資料, 其中輔助訊息與多零值資料是有一定相關性。首先將母體依照其相對應的輔助訊息大小排序, 再平分為四群, 然後用不等機率分別從四群中依次抽出10%, 20%, 40%, 30% 的樣本數。為使擬概度函數可具有不偏性,在此是採用相同權數來建構信賴區間。本文是探討在不同的相關係數ρ和非零值比例α , 及不同非零值母體分布下, 比較傳統方法、最大概度比法以及各種最大擬概度比法在95% 名目水準下, 信賴區間的平均值、標準差和涵蓋率的表現。 The many-zero-observation data in survey sampling under complex probability sampling is considered. The confidence interval derived using the traditional normal approximation based on the central limit theorem (CLT) has poor coverage rate even when the sample size is large. The maximum likelihood method (ML) of Kvanli et al (1998) does not work well either. This paper expands the pseudo likelihood method of Chen and Sitter (1999) that integrated unequal probability sampling design (Cochran, 1977). The method utilizes auxiliary information which has a correlation coefficient ρ with the data. A comparison between different methods was conducted under distinct ρ values and nonzero proportion α, and various nonzero distributions. Simulation results indicate that the pseudo likelihood method improves the coverage rate substantially and outperforms the CLT and ML methods.
