On a class of rank order tests for the identity of two multiple regression surfaces

Summary That the central theorem is valid for (forward) martingales is a result with a long history, beginning with Lévy [6], the most refined and recent results being due to Billingsley [3].Not altogether surprisingly, an analogous result holds for backwards martingales, and the proof, which parallels closely that of Billingsley, occupies Section 1. Examples are given in Section 2.