Title: Intelligent sampling for change point analysis problems
Authors: George Michailidis - University of Florida (United States) [presenting]
Abstract: Change point estimation is traditionally performed by optimizing over the cases of considering each data point as the true location parameter. In truth, only points close to the actual change point provide useful information for estimation, while data points far away are superfluous, to the point where using only a few points close to the true parameter is just as precise as using the full data set. From this principle we constructed a 2-stage method for change point estimation that localizes the analysis to a few small subsamples of the data but is just as accurate as traditional analysis on the full data set. In fact, we demonstrate that this method achieves the same rate of convergence and even virtually the same asymptotic distribution as the analysis of the full data. Furthermore the subsample of data analyzed can be made so small the entire procedure can run in as low as order of root-$N$ time as opposed to at least $O(N)$ time for all current procedures, making it promising for analysis on long data sets with adequately spaced out change points.