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Inference of change-point in single index models

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Abstract

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.

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Authors and Affiliations

  1. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China

    GuanQun Cao, ZhanFeng Wang, YaoHua Wu & LinCheng Zhao

Authors
  1. GuanQun Cao
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  2. ZhanFeng Wang
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  3. YaoHua Wu
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  4. LinCheng Zhao
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Corresponding author

Correspondence to YaoHua Wu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 10471136, 10671189) and the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX3-SYW-S02)

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Cao, G., Wang, Z., Wu, Y. et al. Inference of change-point in single index models. Sci. China Ser. A-Math. 51, 1855–1870 (2008). https://doi.org/10.1007/s11425-007-0170-9

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  • DOI: https://doi.org/10.1007/s11425-007-0170-9

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