A unified and elementary proof of serial and nonserial, univariate and multivariate, Chernoff–Savage results

We provide a simple proof that the Chernoff–Savage [H. Chernoff, I.R. Savage, Asymptotic normality and efficiency of certain nonparametric tests, Ann. Math. Statist. 29 (1958) 972–994] result, establishing the uniform dominance of normal-score rank procedures over their Gaussian competitors, also holds in a broad class of problems involving serial and/or multivariate observations. The non-admissibility of the corresponding everyday practice Gaussian procedures (multivariate least-squares estimators, multivariate t-tests and F-tests, correlogram-based methods, multivariate portmanteau and Durbin–Watson tests, etc.) follows. The proof, which generalizes to the multivariate—possibly serial—set-up the idea developed in J.L. Gastwirth, S.S. Wolff [An elementary method for obtaining lower bounds on the asymptotic power of rank tests, Ann. Math. Statist. 39 (1968) 2128–2130] in the context of univariate location problems, allows for avoiding technical convexity and variational arguments.