Universal outlier hypothesis testing is studied in a sequential setting.
Multiple observation sequences are collected, a small subset of which are
outliers. A sequence is considered an outlier if the observations in that
sequence are generated by an "outlier" distribution, distinct from a common
"typical" distribution governing the majority of the sequences. Apart from
being distinct, the outlier and typical distributions can be arbitrarily close.
The goal is to design a universal test to best discern all the outlier
sequences. A universal test with the flavor of the repeated significance test
is proposed and its asymptotic performance is characterized under various
universal settings. The proposed test is shown to be universally consistent.
For the model with identical outliers, the test is shown to be asymptotically
optimal universally when the number of outliers is the largest possible and
with the typical distribution being known, and its asymptotic performance
otherwise is also characterized. An extension of the findings to the model with
multiple distinct outliers is also discussed. In all cases, it is shown that
the asymptotic performance guarantees for the proposed test when neither the
outlier nor typical distribution is known converge to those when the typical
distribution is known.Comment: Proc. of the Asilomar Conference on Signals, Systems, and Computers,
2014. To appea
