| 姓名 |
葉霈彤(Pei-Tung Yeh)
查詢紙本館藏 |
畢業系所 |
統計研究所 |
| 論文名稱 |
百分比資料的迴歸分析之強韌負二項概似函數法
(Robust negative binomial likelihood inferences for regression analysis of percentage data)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 ( 永不開放)
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| 摘要(中) |
針對百分比資料，我們通常假設資料是符合貝他分配(beta distribution)，以進行分析。然而，在實際應用中，往往無法確定資料的真實分配，這可能會導致對感興趣參數的統計推論出現錯誤。
本文運用強韌化負二項實作概似函數，分析百分比資料。
透過模擬和實例分析，我們呈現了強韌華德檢定統計量(robust wald statistics)、強韌分數檢定統計量(robust score statistics)、強韌概似比檢定統計量(robust likelihood ratio statistics)，以及各個檢定的信賴區間(confidence interval)與覆蓋機率(coverage probability)。
我們比較此方法與貝他迴歸模型在分析百分比資料時的差異與優缺點。通過
簡單迴歸說明，當資料為獨立且同分配(independent and identically distributed, iid)時，隨著樣本數增加，能看出貝他迴歸模型在檢定時會產生錯誤。而在非 iid 的迴歸架構下，貝他迴歸模型的參數估計量已會有明顯的錯誤。使用本文提出的方法，即使未知資料的真實分配，我們仍能得到正確的統計推論，且更適用於實際情況。 |
| 摘要(英) |
Percentage data can be analyzed based on beta distribution. However, in practical applications, we often cannot determine the true distribution of the data, which could result in incorrect statistical conclusions regarding the parameters of interest.
This thesis proposes a robust likelihood function method to analyze percentage data. It presents robust Wald statistics and robust score statistics through simulation and case analysis.
We compare the differences, advantages, and disadvantages between this method and the beta model in analyzing percentage data. Using simple regression as an example, when the data are independently and identically distributed (iid), as the sample size increases, it becomes evident that the beta model produces errors during hypothesis testing. In situations where the data are not iid, the parameter estimates from the beta model exhibit significant errors. Our proposed method can make correct statistical inferences even though using a misspecified model. |
| 關鍵字(中) |
★ 強韌概似函數
★ 百分比資料 |
關鍵字(英) |
★ Robust likelihood function
★ Percentage data |
| 論文目次 |
摘要.................................................................................................................................i
Abstract..........................................................................................................................ii
致謝辭...........................................................................................................................iii
目錄...............................................................................................................................iv
表目錄...........................................................................................................................vi
第一章 緒論................................................................................................................1
第二章 文獻回顧........................................................................................................2
2.1 強韌概似函數......................................................................................................2
2.2 貝他迴歸模型......................................................................................................3
第三章 強韌負二項概似函數....................................................................................6
3.1 負二項模型之強韌化..........................................................................................6
3.2 簡單迴歸下之修正項與強韌檢定統計量........................................................ 11
第四章 模擬研究......................................................................................................14
4.1 資料生成............................................................................................................14
4.1.1 貝他分配百分比資料.............................................................................14
4.1.2 伽瑪與韋伯分配百分比資料.................................................................14
4.2 模擬結果............................................................................................................15
第五章 實例分析......................................................................................................53
5.1 實例一................................................................................................................53
5.2 實例二................................................................................................................55
5.3 實例三................................................................................................................58
第六章 結論..............................................................................................................61
參考文獻......................................................................................................................62 |
| 參考文獻 |
[1] Atkinson, A.C. (1985). Plots, Transformations and Regression: An Introduction to Graphical Methods of Diagnostic Regression Analysis. New York: Oxford University
Press.
[2] Cribari-Neto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24.
[3] Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.
[4] Royall, R. M. and Tsou, T. S. (2003). Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. Journal of the Royal
Statistical Society, Series B, 65: 391-404.
[5] Smithson, M. and Verkuilen, J. (2006). A better lemon squeezer? Maximumlikelihood regression with beta-distributed dependent variables. Psychological Methdos, 11, 54–71.
[6] Tsou, T. S. (2015). A universal robust method for analyzing bivariate continuous and proportion data. Journal of Statistical Computation and Simulation, 85: 3700-3707 |
| 指導教授 |
鄒宗山(Tsung-Shan Tsou)
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審核日期 |
2024-7-15 |
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