Structural change detection via penalized regression

This dissertation research addresses how to detect structural changes in stochastic linear models. By introducing a special structure to the design matrix, we convert the structural change detection problem to a variable selection problem. There are many existing variable selection strategies, however, they do not fully cope with structural change detection. We design two penalized regression algorithms specifically for the structural change detection purpose. We also propose two methods involving these two algorithms to accomplish a bi-level structural change detection: they locate the change points and also recognize which predictors contribute to the variation of the model structure. Extensive simulation studies are shown to demonstrate the effectiveness of the proposed methods in a variety of settings. Furthermore, we establish asymptotic theoretical properties to justify the bi-level detection consistency for one of the proposed methods. In addition, we write an R package with computationally efficient algorithms for detecting structural changes. Comparing to traditional methods, the proposed algorithms showcase enhanced detection power and more estimation precision, with added capacity of specifying the model structures at all regimes.