臺灣博碩士論文加值系統

實務上經常發生資料有缺失的情況，導致統計分析工作難以進行，直接刪除具有缺失值的資料可能失去樣本中一些寶貴的資訊，其中一種取而代之的方法便為插補法。比例插補法可分為加權比例插補法以及未加權比例插補法，在過去的文獻中已經作出以下的結論：(1)經由加權比例插補法，可得對於母體均數近似不偏的估計式；(2)經由未加權比例插補法，得到的估計式對於母體均數會有偏誤。Haziza及Rao(2003)提出未加權比例插補法後的偏誤調整估計式，該偏誤調整估計式對於母體均數亦近似不偏。本文嘗試於分層機率抽樣下，每一層均採用Probability Proportional to Size抽出不放回的方式得到樣本，來比較缺失值經由加權比例插補、未加權比例插補後的均數估計量以及偏誤調整估計量在估計每一層母體均數上的表現，進而比較他們在估計整體母體均數上的表現。而樣本來自的母體情況設定為兩種，一種是每層母體均數不同但標準差相同，另一種則是每一層的母體均數和標準差均不同。模擬一百次的結果發現經由未加權比例插補法得到的估計量較接近真正的母體均數，但若比較偏率則是偏誤調整估計量所產生的偏率最小。除了模擬以外，亦使用一分層機率抽樣下得到的資料進行實證分析，發現經由加權比例插補後的均數估計量和偏誤調整估計量兩者結果相近。

In the presence, missing-data occurs frequently. It may loss important information to delete survey units with missing-data. Imputation is one methods to solve missing-data problem. Ratio imputation contains weighted and unweighted alternatives. From previous studies we have the following conclusions: (1) estimator of a population mean under weighted ratio imputation is approximately unbiased and (2) estimator of a population mean under unweighted ratio imputation is biased. Haziza and Rao (2003) proposed a bias-adjusted estimator of population mean under unweighted ratio imputation. Theoretically, this research aims to employ the theory of Haziza and Rao (2003) to obtain a bias-adjusted estimator under stratified sampling with probability proportional to size. A simulation study is conducted with two conditions: (1) each stratum has different means but with same standard errors and (2) each stratum has different means and with different standard error. The simulation results find that the bias-adjusted estimator has smallest bias ratio. In practice, a set of real data obtained from a survey under stratified sampling with probability proportional to size is also studied. According to the result we found that estimates of a population mean under weighted ratio imputation is similar to bias-adjusted estimates.

目 錄
中文提要 Ⅰ
英文提要 Ⅱ
謝辭 Ⅲ
目錄 Ⅳ
表次 Ⅵ
圖次 Ⅶ
第一章、緒論 1
第一節 研究動機與背景 1
第二節 研究目的及內容 2
第三節 研究架構 3
第二章、文獻回顧 4
第一節 資料缺失的型態 4
第二節 處理缺失值的方法 6
第三節 比例插補法 8
第四節 插補後的估計式及其偏誤 10
第五節 變異數估計式 14
第六節 PPS without Replacement抽樣方法 21
第三章、研究方法 22
第一節 研究方法 22
第二節 模擬流程 27
第四章、模擬結果與實證分析 29
第一節 模擬結果 29
第二節 實證分析 38
第五章、結論與建議 42
參考文獻 45
附表一 回收廢家電的營運成本(元)及回收量(台) 46

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