二段隨機抽樣估計式之模擬研究

抽樣調查以有限人力及經費，獲得所需資訊，為近年來應用甚廣的學科；惟一般抽樣調查偏重於抽樣方法之設計，忽略估計式的選擇，事實上選擇適當的估計式可減少抽樣誤差的產生，對講求效率與準確度的抽樣調查而言，其重要性不下於抽樣方法的設計。　　本研究要旨首先探討（SRS,STS）二段隨機抽樣設計的理論，由於理論驗證困難，因此，本文以模擬分析，比較在某些母體特徵情況下估計值的大小，期望選擇適當估計式使調查結果之抽樣誤差減少，並提高可信度。　　本研究內容摘要如下：　1.探討母體平均數的估計式。　2.探討母體平均數估計量之變異數的估計值。　3.模擬與比較常數配置、比例配置、紐曼配置之變異數估計值。　4.藉由理論和模擬分析，比較（SRS,STS）二段隨機抽樣法變異數之差異。

關鍵字

二段抽樣；模擬

並列摘要

Sampling survey, through which all the information needed is obtained by means of limited personnel and expenditure, has become a widely-applied science recently. Generally, people overemphasize the designing of sampling methods, instead of the choosing of the estimators which, as a matter of fact, decreases sampling errors and is therefore supposed to be as important as the designing of sampling methods. The object of this study is first to investigate the theory of two-stage random sampling design. Since it is very difficult to prove theoretically, we hope to choose suitable estimators, to diminish sampling errors, and to elevate accuracy in itself, while we try to compare, in a simulative way, the applicability of the estimators under certain conditions of population characteristics. The summaries of this thesis are as follows： 1. To confer the estimator of the population mean. 2. To confer the estimator of the variance of the estimator of the population mean. 3. To simulate and compare the estimator of the variance between equal allocation, proportional allocation and Neyman allocation. 4. By theory and simulative analysis, to compare the difference of variance in (SRS,STS) two-stage random sampling.