UMAC is not only provably secure, but is also the fastest-known algorithm to date. We will consider the case of a random walk in Euclidean space. We will examine the case where the random vectors lie in the generalized domain of attraction of a Gaussian law. We are particularly interested in the case where the random vectors under investigation do not have finite second moment. It then becomes important to investigate the effect that extreme values have on the random walk.
Extreme values are ones that dominate the random walk.
We propose two methods for handling extreme values. First, we examine trimming, and give precise conditions on how many extreme values must be trimmed to stabilize the random walk. A second method involves self normalization. Self normalization deals with normalizers that are themselves functions of the data. It has the advantage of being readily computable.