Application of piece-wise regression to detecting internal structure of signal

摘要

The problem of restoring the underlying structure of a signal with the help of piece-wise regression is considered. The case of interest is that the domain of definition of a response function consists of a number of regions of smoothness. The number of regions and the location of change points are not fixed in advance and they should be found by analyzing the signal corrupted with noise. For a given number of smooth regions the best piece-wise regression may be found with the help of an approach based on dynamic programming. The selection of the best model (the best number of regions of smoothness) is performed with the help of a probabilistic estimate. Some properties of the estimate and the whole procedure are studied and the results of experiments are presented.