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上小学 · 2023年08月04日

请问此题如何解答?谢谢

NO.PZ2018122701000058

问题如下:

Which of the following statements about correlation and copula are correct?

I.Copula enables the structures of correlation between variables to be calculated separately from their marginal distributions.

II.Transformation of variables does not change their correlation structure.

III.Correlation can be a useful measure of the relationship between variables drawn from a distribution without a defined variance.

IV.Correlation s a good measure of dependence when the measured variables are distributed as multivariate elliptical.

选项:

A.

I and IV only

B.

II, III, and IV only

C.

I and III only

D.

II and IV only

解释:

A is correct.

考点 Copula Functions

解析

"I" is true. Using the copula approach, we can calculate the structures of correlation between variables separately from the marginal distributions. "IV" is also true. Correlation is a good measure of dependence when the measured variables are distributed as multivariate elliptical.

"II" is false. The correlation between transformed variables will not always be the same as the correlation between those same variables before transformation. Data transformation can sometimes alter the correlation estimate. "III" is also false. Correlation is not defined unless variances are finite.

我认为除了A都是对的,答案恰恰相反。A肯定不对啊。COPULA是求联合概率的,怎么是求单独的呢?其他选项为什么错误呢?

1 个答案

pzqa27 · 2023年08月04日

嗨,从没放弃的小努力你好:


I说的是copula 可以根据每个变量的marginal distribution(概率密度函数)去计算他们的相关系数structure。比如Gaussian copula就是利用标准正态分布去计算相关系数的结构。


II说的是copula函数涉及的数据转换不会改变原始变量的相关系数,这显然是不对的,因为copula是利用正态分布函数去刻画correlation structure,原始的correlation是改变了的。


III说的也不对。如果两个变量的方差是无限大的话,那么相关系数是不存在的。


IV里面的elliptical意思是参数有限、形态固定的分布,例如正态分布这种。参数有限的分布才能去算出来correlation.

.



关于copula重点看经典题里面的考察,基础班讲义P121-124有提到copula的知识点。另外Notes P108-109也有提及copula的考点:



A copula creates a joint probability distribution between two or more variables while maintaining their individual marginal distributions. This is accomplished by mapping multiple distributions to a single multivariate distribution.


Therefore, a copula is a way to indirectly define a correlation relationship between two variables when it is not possible to directly define a correlation.

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