Financial Risk Manager Part 1
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Which of the following statements is (are) correct?
I. The Spearman's approach is also known as the Pearson correlation coefficient for ranked variables.
II. Both the Spearman's and the Kendall measures are nonparametric. They both use the numerical values of the elements in the formula for calculating the correlation coefficient, not the rating of the elements.
III. For calculating Kendall's τ, finding the number of concordant pairs and number of discordant pairs is necessary.
Other
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NNikitesh
A
I, II and III
B
I and III
C
I and II
D
II and III
Explanation:
Explanation:
Statement I is correct: Spearman's correlation coefficient is indeed sometimes referred to as the Pearson correlation coefficient for ranked variables. It applies Pearson's formula to the ranks of the data rather than the raw values.
Statement II is incorrect: While both Spearman's and Kendall's measures are nonparametric, they do NOT use the numerical values of the elements. Instead, they use the ranking (ordinal positions) of the elements. Spearman's uses the ranks directly, while Kendall's τ is based on concordant and discordant pairs of rankings.
Statement III is correct: For calculating Kendall's τ, the formula is:
τ = (nc - nd) / [n(n-1)/2]
Where:
- nc = number of concordant pairs (pairs that have the same ordering in both variables)
- nd = number of discordant pairs (pairs that have opposite ordering in both variables)
- n = number of observations
Finding the number of concordant and discordant pairs is indeed necessary for calculating Kendall's τ.
Therefore, only statements I and III are correct, making option B the correct answer.
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