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I have a probably stupid question, but it's a real mix-up in my head.

When we do econometric analysis for large datasets we say normality of the residuals is not necessary because of the central limit theorem and t-test converges to a standard z-test. But isn't t-test based on a special case of Cauchy distribution that fails in the central limit theory?

Nonparametric tests (e.g. Wilcoxon) were invented to walk around this problem of the t-test, weren't they? Why don't we see Wilcoxon in Econometrics and use the asymptotic normality assumption?

I'm sorry if I make no sense. Got really confused by that

Alex
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    The standard Cauchy distribution coincides with the Student's t-distribution with one degree of freedom. But with large datasets you should have many more than one degree of freedom, and as the number of degrees of freedom increases, the Student's t-distribution approaches a normal Gaussian distribution. – Henry Jan 28 '14 at 22:52
  • The Wilcoxon test is less efficient than the t-test. So as soon as the data set is sufficiently large, people prefer the latter. – Nameless Jan 29 '14 at 00:49

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