A Unified and Elementary Proof of Serial and Nonserial, Univariate and Multivariate, Chernoff-Savage Results

We provide a simple proof that the Chernoff-Savage [1] 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—setup the idea developed in Gastwirth and Wolff [2] in the context of univariate location problems, allows for avoiding technical convexity and variational arguments.