Information Criterion and Change Point Problem for Regular Models

摘要

Information criteria axe commonly used for selecting competing statistical models. They do not favour the model which gives the best fit to the data and little interpretive value, but simpler models with good fit. Thus, model complexity is an important factor in information criteria for model selection. Existing results often equate the model complexity to the dimension of the parameter space. Although this notion is well founded in regular parametric models, it lacks some desirable properties when applied to irregular statistical models. We refine the notion of model complexity in the context of change point problems, and modify the existing information criteria. The modified criterion is found consistent in selecting the correct model and has simple limiting behaviour. The resulting estimator τ of the location of the change point achieves the best convergence rate O_P(1), and its limiting distribution is obtained. Simulation results indicate that the modified criterion has better power in detecting changes compared to other methods.