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Information criterion and change point problem for regular models. (English) Zbl 1193.62004
Summary: Information criteria are 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 to be consistent in selecting the correct model and has simple limiting behaviour. The resulting estimator $$\hat \tau$$ 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.

##### MSC:
 62B99 Sufficiency and information 62B15 Theory of statistical experiments 62B10 Statistical aspects of information-theoretic topics 62E20 Asymptotic distribution theory in statistics 65C60 Computational problems in statistics (MSC2010)
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