The following outlier hypothesis testing problem is studied in a universal setting. Vector observations are collected each with $Mgeq 3$ coordinates, a small subset of which are outlier coordinates. When a coordinate is an outlier, the
observations in that coordinate are assumed to be distributed according to an “outlier” distribution, distinct from the “typical” distribution governing the observations in all the other coordinates. Nothing is known about the outlier and
typical distributions except that they are distinct and have full supports. The goal is to design a universal test to best discern the outlier coordinate(s). We show that it is possible to construct exponentially consistent tests for this problem under various settings.