Principal Fitted Component (PFC) is a semi-parametric sufficient dimension reduction (SDR) method, which is originally proposed in Cook (2007). According to Cook (2007), the PFC has a connection with other usual non-parametric SDR methods. The connection is limited to sliced inverse regression (Li, 1991) and ordinary least squares. Since there is no direct comparison between the two approaches in various forward regressions up to date, a practical guidance between the two approaches is necessary for usual statistical practitioners. To fill this practical necessity, in this paper, we newly derive a connection of the PFC to covariance methods (Yin and Cook, 2002), which is one of the most popular SDR methods. Also, intensive numerical studies have done closely to examine and compare the estimation performances of the semi and non-parametric SDR methods for various forward regressions. The founding from the numerical studies are confirmed in a real data example.
|Number of pages||13|
|Journal||Communications for Statistical Applications and Methods|
|State||Published - 2022|
Bibliographical noteFunding Information:
For Minju Shin and Jae Keun Yoo, this work was supported by the MSIT (Ministry of Science, ICT), Korea, under the High-Potential Individuals Global Training Program (RS-2022-00154879) supervised by the IITP (Institute for Infor-mation & Communications Technology Planning & Evaluation). For Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (NRF-2021R1F1A1059844). 1Corresponding author: Department of Statistics, Ewha Womans University, 52, Ewhayeodae-gil, Seodaemun-Gu, Seoul 03760, Korea. E-mail: email@example.com
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- Covariance methods
- Principal fitted component
- Semi-parametric dimension reduction
- Sufficient dimension reduction