多項分布 2 × 2 列聯表勝算比之區間估計

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吳晨瑄(CHEN-HSUAN WU) 查詢紙本館藏

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統計研究所

論文名稱

多項分布 2 × 2 列聯表勝算比之區間估計
(Interval estimation for the odds ratio of a 2 × 2 contingency table from multinomial distribution)

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摘要(中)

在多項抽樣模型下得到的 2 × 2列聯表，欲想了解兩變數間的關聯強度，通常是對勝算比做區間估計，因此模型抽樣會存在兩個干擾參數，常用正確條件法及正確非條件法來解決。由於正確條件法是給定條件下建構信賴區間，在小樣本下樣本空間會有高度離散的情形，所以區間常具有保守性；正確非條件法是利用最大化條件法來消除干擾參數，其建構出的正確非條件信賴區間會有最短的區間長度，且覆蓋機率至少能達到並接近給定的名目信賴係數，且即使在小樣本至中小樣本中其表現亦如此。

摘要(英)

For a 2 × 2 contingency table sampled from multinomial distribution, we are interested in measuring strength of association between two variables by the odds ratio. Also constructing a confidence interval for the odds ratio is primarily of concerned in practice. For the multinomial sampling, there are two nuisance parameters except for the odds ratio. Hence we usually take the exact conditional approach to obtain a confidence interval for the odds. However, the exact conditional confidence interval can be very conservative because the exact conditional approach may use a high discrete conditional distribution when the sample size is small. On the other hand, the exact unconditional approach eliminates the nuisance parameters by taking the maximal p-value over all possible values of the nuisance parameters. In this paper, we take the unconditional approach to obtain a modified confidence interval. For small to moderate sample sizes, numerical studies show that comparing to other interval the modified confidence interval usually has shorter length, and its actual confidence coefficient is closer to and at least the nominal confidence coefficient.

關鍵字(中)

★ 區間估計
★ 正確非條件方法
★ 正確條件方法
★ 多項式分布
★ 勝算比

關鍵字(英)

★ Interval estimation
★ Multinomial distribution
★ Exact conditional approach
★ Exact unconditional approach
★ Odds ratio

論文目次

1 緒論 1
1.1 研究動機與文獻回顧. . . . . . . . . . . . . . . . 1
1.2 研究目的. . . . . . . . . . . . . . . . . . . . . 5
2 研究方法 6
2.1 p-值與區間估計. . . . . . . . . . . . . . . . . .6
2.2 正確條件信賴區間. . . . . . . . . . . . . . . . . 7
2.3 正確非條件信賴區間. . . . . . . . . . . . . . . . 13
3 數值方法 16
3.1 信賴區間的演算法. . . . . . . . . . . . . . . . . 16
3.1.1 正確條件信賴區間. . . . . . . . . . . . . . . . 16
3.1.2 正確非條件信賴區間. . . . . . . . . . . . . . . 18
3.2 覆蓋機率比較. . . . . . . . . . . . . . . . . . . 21
3.3 期望對數長度比較. . . . . . . . . . . . . . . . . 25
3.4 實例研究. . . . . . . . . . . . . . . . . . . . . 27
4 結論 30
參考文獻 32
附錄1 35
附錄2 43

參考文獻

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指導教授

楊明宗(Ming-Chung Yang)

審核日期

2008-6-26

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