On-line control of false discovery rates for multiple datastreams

Although some false discovery rate control procedures have been proposed in the continual surveillance of high dimensional datastreams, most of them ignore the sequential feature over the time domain and dependence information among the stream observations. This inspires us to exploit the sequential feature by restricting the ongoing streams at each time point to be a dynamic set, which is determined by previous complex controlling procedures. Based on the exponentially weighted moving average (EWMA) scheme, we develop a dynamic multiple testing procedure for high dimensional datastreams with the control of false discovery rates (FDR). The FDR is shown to be controlled pointwise under the condition that the average of correlations of the stream observations decreases to zero at a polynomial rate. Numerical results illustrate that the proposed method is able to deliver satisfactory control performance.