Application of modified information criterion to multiple change point problems |
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Authors: | Jianmin Pan Jiahua Chen |
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Institution: | aDepartment of Biostatistics, St. Jude Children's Research Hospital, Memphis, TN 38105, USA;bDepartment of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 |
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Abstract: | The modified information criterion (MIC) is applied to detect multiple change points in a sequence of independent random variables. We find that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We show that the estimators for locations of change points achieve the best convergence rate, and their limiting distribution can be expressed as a function of a random walk. A simulation is conducted to demonstrate the usefulness of this method by comparing the powers between the MIC and the Schwarz information criterion. |
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Keywords: | Consistency Convergence rate Limiting distribution Multiple change points Model complexity Regular parametric model |
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