Segment regression model average with multiple threshold variables and multiple structural breaks

We propose a new model averaging approach to investigate segment regression models with multiple threshold variables and multiple structural breaks. We first fit a series of models, each with a single threshold variable and multiple breaks over its domain, using a two-stage change point detection method. Then these models are combined together to produce a weighted ensemble through a frequentist model averaging approach. Consequently, our segment regression model averaging (SRMA) method may help identify complicated subgroups in a heterogeneous study population. A crucial step is to determine the optimal weights in the model averaging, and we follow the familiar non-concave penalty estimation approach. We provide theoretical support for SRMA by establishing the consistency of individual fitted models and estimated weights. Numerical studies are carried out to assess the performance in low- and high-dimensional settings, and comparisons are made between our proposed method and a wide range of existing alternative subgroup estimation methods. Two real economic data examples are analyzed to illustrate our methodology.