Explanation

Let's analyze each option:

Option A: Incorrect A zero Pearson correlation only indicates no linear relationship. There could still be non-linear relationships present.

Option B: Incorrect Spearman rank correlation and Kendall's τ measure monotonic relationships, not all types of non-linear relationships. They cannot detect non-monotonic non-linear relationships.

Option C: Correct

• Pearson correlation: Measures linear dependence between variables
• Spearman rank correlation: Measures monotonic relationships (whether linear or non-linear, as long as the relationship is consistently increasing or decreasing)
• Kendall's τ: Also measures monotonic relationships, similar to Spearman but using a different calculation method

Option D: Incorrect Significant differences between Pearson and rank correlations actually suggest the presence of non-linear relationships, not their absence.

Therefore, option C is the correct statement.