新版巴賽爾資本協定的內部評等法中，銀行可自行對借貸戶進行評分，並且根據 評分估算信用風險以提領準備金，因此估算借貸戶評分分數的違約機率(PD)是相當 重要的一環。過去估算違約機率的研究中，大多假定評分分數為離散型式，本文針對 評分分數為連續形式時，提出一種利用曲線函數來配適估計模型。估計模型是使用伽 瑪的截尾分配去配適ROC曲線函數，再利用此ROC曲線函數來估計各評分分數下的 違約機率P(D|S)，在伽瑪分配中的兩參數則是用兩階段的方法求解。本文所提的估 計方法並無假設評分分數的分配，因此在數值方法中使用不同的分配、參數設定、違 約機率等，來驗證此方法的準確度與穩定度，並且與Van der Burgt (2008)、Tasche(2009)的估計方法比較。 / By the internal rating-based approach of Basel II, banks estimate borrowers' default risks to withdraw reserves independently. Hence, estimating default probability (PD) of borrowers is important. Most of previous studies estimating PD assume that evaluation scores are discrete, In this study, we use curve function to t estimation model in the condition that the evaluation scores are continuous . We use truncated gamma distribution to t ROC curve function. And we use the ROC curve function to estimate PD of dierent scores. And use two-step method to nd the value of two parameters in gamma distribution. The estimation method in this study doesn't assume the distribution of estimation scores,so we use dierent distributions, parameters, and default probabilities to test the accuracy and stability of this method. In the end, we also compare our methods with Van der Burgt (2008) and Tasche (2009)' methods.

表面增強雷射脫附遊離/飛行時間質譜(SELDI-TOF-MS)是種屬於高維度的蛋白質質譜儀資料，主要是用來偵測蛋白質分子的表現。由於SELDI技術的限制，導致掃描出來的質譜儀資料往往存在誤差與雜訊，因此在分析前通常會先針對原始資料進行低階的事前處理，步驟包括去除基線、正規化、峰偵測(peak detection)與峰調準(peak alignment)。本文中所探討前列腺癌資料，可分成正常、良性腫瘤、癌症初期與癌症末期四種類別。我們分析及比較兩筆事前處理的蛋白質質譜資料，包括我們自行處理的以及Adam等人所處理的資料。為了解決SELDI在偵測分子質量時常出現的位移誤差以及同位素的問題，我們提出以”質荷比段落”當作新的特徵變數的想法來進行分析。本文利用「ROC曲線下面積」(AUC)當作選取的準則來挑選出重要的質荷比段落，而分類方法則採用支援向量機(SVM)。在四分類的分類結果中，我們自行處理的事前處理資可以得到訓練資料89%及測試資料63 %的正確率。而Adam等人所處理的事前處理資料，則得到訓練資料94%及測試資料86 %的正確率。本研究結果指出不同事前處理的方法對分類結果確實有影響，同時也驗證了利用”特徵變數段落”的方法來進行分析的可行性。 / The surface enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) is a technique for presenting the expression of molecular masses. It is obvious that every spectrum has a huge dimension of features. In order to analyze these types of spectra samples, preprocessing steps are necessary. The steps of preprocessing include baseline subtraction, normalization, peak detection, and alignment. In our study, we use a prostate cancer data for demonstration. This prostate cancer data can be classified into four categories, namely, healthy men, benign prostate hyperplasia, early stage prostate cancer, and late stage prostate cancer. We analyzed both the preprocessed data processed by ourselves and the preprocessed data done by Adam et al.. In this thesis, we use segmentations of features as “new features” in attempt to solve problems due to location shifts and isotopes. The selection of important segmentations was based on the values of AUC and the SVM was applied for classification. For four-class classification, 94 % and 86 % of accuracy were obtained for training samples and validation samples, respectively, by using Dr. Adam et al.’s preprocessed data, and 89% for training samples, and 63% for validation samples by using our preprocessed data. This study suggested that the preprocessed method does have effect on classification result and a reasonable classification result can be obtained by using segmentations of features.