Abstract:
|
In threshold and location estimation one often tries to minimize over a set of location and auxiliary parameters, with the former adding computational time to what can be otherwise simple optimization schemes. We introduce a general 2-stage sampling scheme for observed databases and time-series, which we coin 'intelligent sampling', which aims to estimate parameters using an appropriately chosen subsample of the data. Ideally this method can yield optimal convergence rates using a vanishing fraction of the entire dataset, and our analysis of several change point problems support this hypothesis. We can demonstrate that in the single change point model, intelligent sampling achieves the optimal 1/N rate of convergence by only analyzing a subsample of N^(1/2) points from the full dataset. Furthermore, we explore the possibility of adapting this methodology to the multiple change point models and change-planes models in higher dimensions.
|