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題名 混合分配下之估計模型鑑別力比較
Comparison of Estimating Discriminatory Power under Mixed Model作者 廖雅薇 貢獻者 劉惠美<br>陳麗霞
廖雅薇關鍵詞 模型鑑別力
AUC
核
EM演算法
偏斜常態分配
Discrimination
AUC
Kerne
EM
Skewed normal distribuion日期 2009 上傳時間 5-Sep-2013 15:14:20 (UTC+8) 摘要 銀行在評分模型建置完成後需進行驗證工作，以瞭解評分模型是否能有效評出客戶的風險層級，穩健地估計區別鑑別力指標為驗證工作中的重點。在先前的文獻中假設正常授信戶與違約戶分數分配為常態分配。但在實際資料中，分配未必定為常態。因此本文接著探討在正常授信戶與違約授信戶之分配為混合分配，即兩分數分配為偏斜常態分配下，何種方法可以對於估計AUC具有較高的穩定性。本文比較五種估計AUC的方法，分別為常態核，經驗分配，曼惠尼近似，最大摡似法和EM演算法。模擬結果呈現(1)投信戶組合分配為兩常態分配下，最大摡似法在大部分違約率下都可以得到較窄的信賴區間。(2)組合分配為一常態與一偏斜常態及兩偏斜常態分配下，EM演算法在大部分情況有較窄的信賴區間，其中在兩偏斜常態分配下，表現更佳。(3)曼惠尼近似建構的信賴區間寬度最大，代表曼惠尼近似是較保守的估計方法。
Banks face discrimination after constructing the rating systems to figure out whether the systems can discriminate defaulting and non-defaulting borrowers. Literature assumed the two score distribuion are normal distributed. However, the real data may not be normal distribuions. We assum the two score distribuions are skewed normal distribuions to discuss which method has more robustness to estimate the AUC value.Under skewed distribution, we propose EM algorithm to estimate the population parametric. If used properly, information about the population properties may be used to get better accuracy of estimation the AUC value.Numerical results show the EM algorithm method , comparing with other methods, has robustness in detect the rating systems have discirmatory power.參考文獻 邱嬿燁(2008)"探討單因子複合分配關聯結構模型之擔保債權憑證之評價",國立政治大學碩士論文Arellano-Valle, R.B., Gomez, H.W., and Quintana, F.A. (2004), “A new class of skew-normal distributions”, Communications in Statistics-Theory and Methods,33(7),1465-1480.Azzalini,A.(2005), “The skew-normal distribution and related multivariate families”,Scandinavian Journal of Statistics, 32(2),159-188.Davison, A.C. and Hinkley, DV (1997), Bootstrap methods and their application, Cambridge Univ Pr.Engelmann, B., Hayden, E., and Tasche, D. (2003a), “Measuring the discriminative power of rating systems”, Deutsche BundesBank, 1-24.------(2003b), “Testing rating accuracy”, Risk, 16(1), 82-86.Genton, Marc G. (2005), “Discussion of The Skew-normal”, Scandinavian Journal of Statistics, 32, 189-198.Gonzalez-Farias, G.,Dominguez-Molina, A., and Gupta, A.K. (2004), “Additive properties of skew normal random vectors”, Journal of Statistical Planning and Inference, 126(2), 521-534.Hosmer, D.W. and Lemeshow, S. (2000), Applied logistic regression, Wiley-Interscience.Pagan and Ullah, A. (1999), Nonparametric econometrics, Cambridge University Press.Satchell and Xia., W. (2008), Analytic models of the ROC curve: Applications to credit rating model validation. In G. Christodoulakis and S. Satchell, editors, The Analytics of Risk Model Validation, Academic Press.Tasche, Dirk (2005), “Studies on the Validation of Internal Rating Systems(revised)”, Quantitative Finance Papers.-----(2009), “Estimating discriminatory power and PD curves when the number of defaults is small”, Bank for International Settlements.Vidakovic, Brani (2003), “EM Algorithm and Mictures.”, Citeseer. 描述 碩士
國立政治大學
統計研究所
97354010
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0973540101 資料類型 thesis dc.contributor.advisor 劉惠美<br>陳麗霞 zh_TW dc.contributor.author (Authors) 廖雅薇 zh_TW dc.creator (作者) 廖雅薇 zh_TW dc.date (日期) 2009 en_US dc.date.accessioned 5-Sep-2013 15:14:20 (UTC+8) - dc.date.available 5-Sep-2013 15:14:20 (UTC+8) - dc.date.issued (上傳時間) 5-Sep-2013 15:14:20 (UTC+8) - dc.identifier (Other Identifiers) G0973540101 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60449 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 97354010 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) 銀行在評分模型建置完成後需進行驗證工作，以瞭解評分模型是否能有效評出客戶的風險層級，穩健地估計區別鑑別力指標為驗證工作中的重點。在先前的文獻中假設正常授信戶與違約戶分數分配為常態分配。但在實際資料中，分配未必定為常態。因此本文接著探討在正常授信戶與違約授信戶之分配為混合分配，即兩分數分配為偏斜常態分配下，何種方法可以對於估計AUC具有較高的穩定性。本文比較五種估計AUC的方法，分別為常態核，經驗分配，曼惠尼近似，最大摡似法和EM演算法。模擬結果呈現(1)投信戶組合分配為兩常態分配下，最大摡似法在大部分違約率下都可以得到較窄的信賴區間。(2)組合分配為一常態與一偏斜常態及兩偏斜常態分配下，EM演算法在大部分情況有較窄的信賴區間，其中在兩偏斜常態分配下，表現更佳。(3)曼惠尼近似建構的信賴區間寬度最大，代表曼惠尼近似是較保守的估計方法。 zh_TW dc.description.abstract (摘要) Banks face discrimination after constructing the rating systems to figure out whether the systems can discriminate defaulting and non-defaulting borrowers. Literature assumed the two score distribuion are normal distributed. However, the real data may not be normal distribuions. We assum the two score distribuions are skewed normal distribuions to discuss which method has more robustness to estimate the AUC value.Under skewed distribution, we propose EM algorithm to estimate the population parametric. If used properly, information about the population properties may be used to get better accuracy of estimation the AUC value.Numerical results show the EM algorithm method , comparing with other methods, has robustness in detect the rating systems have discirmatory power. en_US dc.description.tableofcontents 誌謝 i中文摘要 ii英文摘要 iii目錄 iv表目錄 vi圖目錄 viii第一章緒論 1第一節研究背景與目的 1第二節研究內容與架構 2第二章文獻探討 3第一節區別模型判別力指標 3(一)CAP及AR 3(二)ROC及AUC 5(三)判別力的基本理論 7第二節偏斜常態分配 8第三節多變量封閉偏斜常態分配 10第三章研究方法 12第一節混合分配下的理論AUC值 12第二節估計AUC方法 13(一)常態核機率密度函數(normal kerner density)估計 13(二)經驗分配(empirical distribution)機率密度函數估計 15(三)Mann-Whitney漸近常態估計法 17(四)在假設母體為常態分配下利用最大概似估計法估計母體參數以估計AUC值 18(五)利用EM方法估計參數以估計AUC值 19 第三節評估不同估計AUC方法穩定性的準則 20第四章模擬結果 22第一節信賴區間計算 22第二節準則設定 22第三節混合模型下授信戶組合介紹 23第四節模擬結果分析與比較 27第五章結論 39參考文獻 40 zh_TW dc.format.extent 1237694 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0973540101 en_US dc.subject (關鍵詞) 模型鑑別力 zh_TW dc.subject (關鍵詞) AUC zh_TW dc.subject (關鍵詞) 核 zh_TW dc.subject (關鍵詞) EM演算法 zh_TW dc.subject (關鍵詞) 偏斜常態分配 zh_TW dc.subject (關鍵詞) Discrimination en_US dc.subject (關鍵詞) AUC en_US dc.subject (關鍵詞) Kerne en_US dc.subject (關鍵詞) EM en_US dc.subject (關鍵詞) Skewed normal distribuion en_US dc.title (題名) 混合分配下之估計模型鑑別力比較 zh_TW dc.title (題名) Comparison of Estimating Discriminatory Power under Mixed Model en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 邱嬿燁(2008)"探討單因子複合分配關聯結構模型之擔保債權憑證之評價",國立政治大學碩士論文Arellano-Valle, R.B., Gomez, H.W., and Quintana, F.A. (2004), “A new class of skew-normal distributions”, Communications in Statistics-Theory and Methods,33(7),1465-1480.Azzalini,A.(2005), “The skew-normal distribution and related multivariate families”,Scandinavian Journal of Statistics, 32(2),159-188.Davison, A.C. and Hinkley, DV (1997), Bootstrap methods and their application, Cambridge Univ Pr.Engelmann, B., Hayden, E., and Tasche, D. (2003a), “Measuring the discriminative power of rating systems”, Deutsche BundesBank, 1-24.------(2003b), “Testing rating accuracy”, Risk, 16(1), 82-86.Genton, Marc G. (2005), “Discussion of The Skew-normal”, Scandinavian Journal of Statistics, 32, 189-198.Gonzalez-Farias, G.,Dominguez-Molina, A., and Gupta, A.K. (2004), “Additive properties of skew normal random vectors”, Journal of Statistical Planning and Inference, 126(2), 521-534.Hosmer, D.W. and Lemeshow, S. (2000), Applied logistic regression, Wiley-Interscience.Pagan and Ullah, A. (1999), Nonparametric econometrics, Cambridge University Press.Satchell and Xia., W. (2008), Analytic models of the ROC curve: Applications to credit rating model validation. In G. Christodoulakis and S. Satchell, editors, The Analytics of Risk Model Validation, Academic Press.Tasche, Dirk (2005), “Studies on the Validation of Internal Rating Systems(revised)”, Quantitative Finance Papers.-----(2009), “Estimating discriminatory power and PD curves when the number of defaults is small”, Bank for International Settlements.Vidakovic, Brani (2003), “EM Algorithm and Mictures.”, Citeseer. zh_TW
