  We propose a general and flexible procedure for testing multiple hypotheses
about sequential (or streaming) data that simultaneously controls both the
false discovery rate (FDR) and false nondiscovery rate (FNR) under minimal
assumptions about the data streams which may differ in distribution, dimension,
and be dependent. All that is needed is a test statistic for each data stream
that controls the conventional type I and II error probabilities, and no
information or assumptions are required about the joint distribution of the
statistics or data streams. The procedure can be used with sequential, group
sequential, truncated, or other sampling schemes. The procedure is a natural
extension of Benjamini and Hochberg's (1995) widely-used fixed sample size
procedure to the domain of sequential data, with the added benefit of
simultaneous FDR and FNR control that sequential sampling affords. We prove the
procedure's error control and give some tips for implementation in commonly
encountered testing situations.
