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wilsonxu · 2021年08月24日

老师,麻烦再解释一下D,没有看懂,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.

老师,麻烦再解释一下D,没有看懂,谢谢!

1 个答案
已采纳答案

DD仔_品职助教 · 2021年08月24日

嗨,从没放弃的小努力你好:


同学你好,


D选项中的II是错误的,II说变量的转换是不会改变他们之间的相关性结构。

变量的转换是指,例如将price转换为ln(price),那么原本变量price之间的相关性,和变量转换之后的ln(price)的相关性有可能是不一样的。所以相关性结构会改变。


IV是正确的,IV说当变量是服从多元椭圆分布的时候,相关性可以很好地衡量dependence也就是数据之间的依赖程度。

多元椭圆分布其实是一个立体的正态分布,看到他时可以直接近似于正态分布。对于服从正态分布的数据,是可以用相关性correlation来衡量他们之间的关系的。那么服从多元椭圆分布的数据也就可以用correlation衡量数据间的关系。


这两句话可以当做结论来记忆~

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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