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| Title: | 信用違約機率的聯合校準檢定
Joint Calibration Test of Credit Rating Probabilities of Default |
| Authors: | 郭書廷
Kuo,Shu Ting |
| Contributors: | 劉惠美
陳麗霞
Liu,Huimei
Chen,Li Shya
郭書廷
Kuo,Shu Ting |
| Keywords: | 違約機率校準檢定
交聯集檢定
齊一較強檢力檢定
calibration test
intersection union test
uniformly more powerful test |
| Date: | 2009 |
| Issue Date: | 2013-09-05 15:09:46 (UTC+8) |
| Abstract: | 違約機率校準檢定 - global test 由兩部分組成：第一部分為 level，探討真實的平均違約機率是否被高估；第二部分 shape，探討高低違約機率的表現情形。但 global test 與相關違約事件下的 level test 檢定尺度皆遠高於顯著水準 $\\alpha$。本文先是針對相關違約事件，利用截斷分配使 level test 犯型一誤差機率更接近顯著水準，並提出虛無假設及對立假設為 $H_0: \\theta \\in \\cup_{i=1}^2 \\Theta_{i0}$ vs. $H_1: \\theta \\in \\cap_{i=1}^2 \\Theta_{i1}$ 的形式，引用交聯集檢定。更進一步透過 Liu \\& Berger (1995, \\textit{The Annals of Statistics}, 23, 1, 55-72) 建構齊一較強檢力檢定，改善檢定力。模擬結果顯示交聯集檢定與齊一較強檢力檢定的檢定尺度皆為 $\\alpha$，且齊一較強檢力檢定的檢定力皆高於交聯集檢定。
The calibration test of the PDs (probabilities of default) --- global test is twofold, the first part is the level test, which is about the mean of calibrated PDs. Second, the shape test is about whether a calibrated PD model differentiates correctly between low and high default probability events. In simulation results, we found that the type I error of global test is much greater than significant level $\\alpha$, so is level test in correlation default events. In this study, firstly, we use the truncated level test to control previous error and suggest the hypothesis $H_0: \\theta \\in \\cup_{i=1}^2 \\Theta_{i0}$ vs. $H_1: \\theta \\in \\cap_{i=1}^2 \\Theta_{i1}$. Secondly, we introduce the intersection union test (IUT). Moreover, we construct an uniformly more powerful test (UMP test) by Liu \\& Berger (1995, \\textit{The Annals of Statistics}, 23, 1, 55-72). Simulation results show that the IUT and UMP test are size $\\alpha$ tests, and the power of UMP test is greater than IUT. |
| Reference: | Berger, R.L. (1989), “Uniformly more powerful tests for hypotheses concerning linear inequalities and normal means”, Journal of the American Statistical Association, 84(405), 192–199.
Blo ̈chlinger, A., Kantonalbank, Z., and Leippold, M. (2009), “Goodness-of-fit test for event forecasting”, Working paper.
Lehmann, EL (1952), “Testing multiparameter hypotheses”, The Annals of Mathe- matical Statistics, 541–552.
Liu, H. and Berger, R.L. (1995), “Uniformly more powerful, one-sided tests for hypotheses about linear inequalities”, The Annals of Statistics, 23(1), 55–72.
McDermott, Michael P. and Wang, Yining (2002), “Construction of uniformly more powerful tests for hypotheses about linear inequalities”, Journal of Statistical Planning and Inference, 107(1-2), 207 – 217.
Sasabuchi, S. (1980), “A test of a multivariate normal mean with composite hy- potheses determined by linear inequalities”, Biometrika, 67(2), 429.
Wilde, T. (1997), “Creditrisk+: A credit risk management framework”, Credit Suisse First Boston. |
| Description: | 碩士
國立政治大學
統計研究所
97354004
98 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0097354004 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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