  We study an online multiple testing problem where the hypotheses arrive
sequentially in a stream. The test statistics are independent and assumed to
have the same distribution under their respective null hypotheses. We
investigate two procedures LORD and LOND, proposed by (Javanmard and Montanari,
2015), which are proved to control the FDR in an online manner. In some
(static) model, we show that LORD is optimal in some asymptotic sense, in
particular as powerful as the (static) Benjamini-Hochberg procedure to first
asymptotic order. We also quantify the performance of LOND. Some numerical
experiments complement our theory.
