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臧小玉 · 2022年01月08日

一类与二类错误

NO.PZ2018122701000033

问题如下:

Basel II requires a backtest of a bank’s internal value at risk (VaR) model (IMA). Assume the bank’s ten-day 99% VaR is $1 million (minimum of 99% is hard-wired per Basel). The null hypothesis is: the VaR model is accurate. Out of 1,000 observations, 25 exceptions are observed (we saw the actual loss exceed the VaR 25 out of 1000 observations).  (Binomial CDF)

选项:

A.

We will probably call the VaR model good (accurate) but we risk a Type I error.

B.

We will probably call the VaR model good (accurate) but we risk a Type II error.

C.

We will probably call the model bad (inaccurate) but we risk a Type I error.

D.

We will probably call the model bad (inaccurate) but we risk a Type II error.

解释:

C is correct.

考点 : Backtesting VaR

解析 :H0 : the VaR model is accurate. Hα: the VaR model is inaccurate.

Z=xpTp(1p)T=251%×10001%×(11%)×1000=4.77Z=\frac{x-pT}{\sqrt{p(1-p)T}}=\frac{25-1\%\times1000}{\sqrt{1\%\times(1-1\%)\times1000}}=4.77

As 4.77 is larger than 2.58, we reject the null hypothesis. Therefore, the model is bad model, and this implies a risk of type I error.

题干中假设是错误的,就是H0是错误的,针对一个错误的假设不是更容易犯存伪二类错误么?正确选项为什么是拒真的一类错误?
1 个答案

李坏_品职助教 · 2022年01月08日

嗨,努力学习的PZer你好:


对于backtesting var,H0是var model 是正确的,H1是Var model是错误的。

我们算出来的Z值是4.77,拒绝了H0,所以是拒绝了原假设,得出了var模型是bad model的结论。


一类错误的定义是:拒绝了一个本来是正确的H0,所以这个题目中我们有可能犯的是一类错误。


二类错误是在fail to reject H0的时候才会犯。

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