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I am trying survival analysis and it seems like a common consensus that Logrank, Wald and likelihood ratio are asymptotically equivalent

I don't understand why they are asymptotically equivalent. As far as I understand, Logrank is a Wilconxon alike method used on censored data. Wald test is more like the parametric version of alternative of Logrank test. How does likelihood ratio test fit into this problem? Why do people say likelihood ratio test is preferred when sample size is small?

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