Supplementary Material

Review of  Transformations and Jacobians

Convolution Theorem for Normal Experiments
(Proof based on van der Vaart, A. (1991). An asymptotic representation theorem. International Statistical Review 59:97-121.
See Theorem 5.1 of this paper.)

Asymptotic Normality of Rank Tests - End of Proof (verification of Lindeberg condition)

Article on Bartlett correction  (link to campus journal database)

Article on connection between rank tests and logrank-type tests in survival analysis (link to campus journal database)

Gastwirth article on nonparametric tests (link to campus journal database)

MATERIAL RELATED TO WEAK CONVERGENCE THEORY
   Separability Lemma
   Note on measurability in C[a,b]
   Proof of Generalized Continuous Mapping Theorem Using Portmanteau Theorem
   Fidi lemma
   Proofs of the Skohorod Representation Theorem and Prohorov's Theorem
      (taken from Billingsley, 1971, Weak Covergence of Measures: Applications in Probability, SIAM)
   Hahn's Theorem