Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Generalized Partially Double-Index Model: Bootstrapping and Distinguishing Values

  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University)
  • Received : 2015.03.23
  • Accepted : 2015.05.08
  • Published : 2015.05.31
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Abstract

We extend a generalized partially linear single-index model and newly define a generalized partially double-index model (GPDIM). The philosophy of sufficient dimension reduction is adopted in GPDIM to estimate unknown coefficient vectors in the model. Subsequently, various combinations of popular sufficient dimension reduction methods are constructed with the best combination among many candidates determined through a bootstrapping procedure that measures distances between subspaces. Distinguishing values are newly defined to match the estimates to the corresponding population coefficient vectors. One of the strengths of the proposed model is that it can investigate the appropriateness of GPDIM over a single-index model. Various numerical studies confirm the proposed approach, and real data application are presented for illustration purposes.

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References

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  1. Case studies: Statistical analysis of contributions of vitamins and phytochemicals to antioxidant activities in plant-based multivitamins through generalized partially double-index model vol.23, pp.3, 2016, https://doi.org/10.5351/CSAM.2016.23.3.251
  2. Bootstrap methods for long-memory processes: a review vol.24, pp.1, 2017, https://doi.org/10.5351/CSAM.2017.24.1.001