An adaptive SIR method for block-wise evolving data streams

In this communication, we consider block-wise evolving data streams. When a semiparametric regression model involving a common dimension reduction direction B is assumed for each block, we propose an adaptive SIR (for sliced inverse regression) estimator of B. This estimator is faster than usual SIR applied to the union of all the blocks, both from computational complexity and running time points of view. We show the consistency of our estimator at the root-n rate. In a simulation, we illustrate the good numerical behaviour of the estimator. We also provide a graphical tool in order to detect if there exists a drift of the dimension reduction direction or some aberrant blocks of data. We illustrate our approach with various scenarios. Finally, possible extensions of this method are given.