兩階段分層抽樣之樣本配置方式的比較分析

A Comparative Analysis of Sample Allocation Methods with Two-stage Stratified Sampling

許玉雪(Esher Hsu) ； 王晏羚(Yen-Ling Wang)

《統計與資訊評論》 19卷 (2019/12) Pp. 113-143

摘要

常見結合分層隨機抽樣所採用的樣本配置方式只著重整體母體參數估計的精確度，而未考量子母體參數估計的精確度。資料精確度的要求隨著資料需求的增加而提高，精確度的要求也由整體母體參數估計進到子母體參數估計。本文旨在介紹一個同時兼顧子母體參數估計精確度的樣本配置法（簡稱dual approach），比較分析dual approach與一般常用的樣本配置法之差異，進而導出兩階段分層抽樣在兼顧子母體相對精確度的最佳樣本配置式，並以「年低收入戶及中低收入戶生活狀況調查」為例進行實證應用。實證結果顯示本文所提出的dual approach樣本配置結果與一般常用的樣本配置結果有明顯的差異，差異主要是配置式內考量子母體參數估計的精確度。

關鍵字

樣本配置 ； 分層抽樣 ； 兩階段抽樣 ； 內曼配置 ； 特徵問題法

並列摘要

Sample allocation methods commonly used with stratified random sampling in market survey includes proportional allocation, Neyman allocation, and optimum allocation. Basically, they only focus on the precision of estimating the overall population parameters and do not take the precision of estimating subpopulation parameters into account. Estimation precision requirement has been increased along with the increasing data demand. The precision requirement is also extended from the estimation of overall population parameters to the estimation of sub-population parameters. This study intends to present a sample allocation method which takes the precision of estimating sub-population parameters into account. In this study, an allocation formula with two-stage stratified sampling derived from dual approach is presented and compared with general allocation methods, such as proportional allocation, Neyman allocation, and optimum allocation. A practical example is conducted based on the ＂Low-income households living condition survey＂ to show how the proposed allocation method can be used in practice. The empirical results show that the sample allocation based on the dual approach proposed by this study is obviously different from that of the general methods. The differences are mainly due to precision requirement of estimating subpopulation parameters in the formula of sample allocation.

並列關鍵字

Sample allocation ； Stratified sampling ； Two-stage sampling ； Neyman allocation ； Eigenproblem approach