| Summary: | 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.
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