樣本配置方式在子母體參數估計的比較分析-以台灣公務調查統計為例

A Comparative Analysis of Sample Allocation Methods on Estimating Subpopulation Parameters – An Application of Official Survey in Taiwan

王晏羚(YEN-LING WANG)

指導教授 ： 許玉雪

國立臺北大學/商學院/統計學系/碩士(2016年)

摘要

一般而言市場調查結合分層隨機抽樣在進行樣本配置時通常只著重於整個母體參數估計的精確度，未將子母體參數估計的精確度列入考量。當我們要顧及每個子母體也達到一定的精確度時，樣本該如何進行配置是本文研究重點。本文旨在探討同時考量每個子母體的參數估計要達到一定的精確度時，該如何進行樣本配置。首先彙整過去文獻上使用的樣本配置方法，包含一般較常使用的比例配置、黎曼配置以及Wesolowski (2015) 提出的dual approach三種樣本配置方式。進而以民國102「年低收入戶及中低收入戶生活狀況調查」為例，說明以上三種配置方式在此案例之應用及配置結果，並就理論面對這三種樣本配置方式進行比較分析。研究結果顯示dual approach配置方式較比例配置及最佳配置的結果來得好，因dual approach的樣本配置方式除了可以達到整個母體參數估計精確度的要求外也同時滿足子母體參數估計的精確度條件。

關鍵字

Dual approach ； 最佳配置 ； 比例配置 ； 分層抽樣 ； 樣本配置

並列摘要

In general, sample allocation with stratified simple random sampling in market survey only focuses on the precision of estimating whole population parameters, but not takes the precision of estimating subpopulations’ parameters into account. How to allocate the samples when we also claim the precision of the subpopulations is the main purpose of this article. This study intends to summarize the sample allocation methods in previous studies. Three allocation methods, namely, proportional allocation, Neyman allocation, and dual approach are selected for further comparative analysis. This article takes “Low-income households living condition survey” as an example to explain how to allocate the samples by three kinds of allocation methods mentioned above and compares their estimation precision based on previous studies. Study results show that dual approach would be better than the others because dual approach method can not only meet the precision requirement of estimating the whole population parameters but also reach the precision requirement of estimating subpopulations parameter.

並列關鍵字

Proportional allocation ； Stratified sampling ； Sample allocation ； Neyman allocation ； Dual approach

參考文獻

1. 洪永泰,黃永政.台灣地區電話隨機撥號抽樣方法之研究.選舉研究,7 (1), pp 173-194

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7. Olayiwola, O.M., and Apantaku, F.S., and Bisira, H.O., and Adewara, A.A. Efficiency of Neyman Allocation Procedure over other Allocation Procedures in Stratified Random Sampling. American Journal of Theoretical and Applied Statistics.Vol.2,No.5 (2013),pp.122-127

8. Wesolowski, J., and Niemiro, W. Fixed precision optimal allocation in two-stage sampling. Applicationes Mathematicae 28 (2001),pp.73-82