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Estimation and clustering for partially heterogeneous single index model

Author

Listed:
  • Fangfang Wang

    (Shandong University)

  • Lu Lin

    (Shandong Technology and Business University
    Qufu Normal University)

  • Lei Liu

    (Washington University in St. Louis)

  • Kangning Wang

    (Shandong Technology and Business University)

Abstract

In this paper, our goal is to estimate the homogeneous parameter and cluster the heterogeneous parameters in a partially heterogeneous single index model (PHSIM). To achieve the goal, the minimization criterion for such a single index model is first transformed into a least-squares optimization problem in the population form. Based on the least-squares objective function, we introduce an empirical version for the PHSIM. By minimizing such an empirical version, we estimate the homogeneous parameter and the subgroup-averages of the heterogeneous index directions, and then use a fusion penalized method to identify the subgroup structure of the PHSIM. By the proposed methodologies, the homogeneous parameter and the heterogeneous index directions can be consistently estimated, and the heterogeneous parameters can be consistently clustered. Moreover, the new clustering procedure is simple and robust. Simulation studies are carried out to examine the performance of the proposed methodologies.

Suggested Citation

  • Fangfang Wang & Lu Lin & Lei Liu & Kangning Wang, 2021. "Estimation and clustering for partially heterogeneous single index model," Statistical Papers, Springer, vol. 62(6), pages 2529-2556, December.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:6:d:10.1007_s00362-020-01203-2
    DOI: 10.1007/s00362-020-01203-2
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    References listed on IDEAS

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