Intensive comparison of semi-parametric and nonparametric dimension reduction methods in forward regression

Minju Shin; Jae Keun Yoo

doi:10.29220/CSAM.2022.29.5.615

Intensive comparison of semi-parametric and nonparametric dimension reduction methods in forward regression

Minju Shin, Jae Keun Yoo

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	615-627
Number of pages	13
Journal	Communications for Statistical Applications and Methods
Volume	29
Issue number	5
DOIs	https://doi.org/10.29220/CSAM.2022.29.5.615
State	Published - 2022

Bibliographical note

Funding 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: peter.yoo@ewha.ac.kr

Publisher Copyright:
© 2022 The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.

Keywords

Covariance methods
Principal fitted component
Semi-parametric dimension reduction
Sufficient dimension reduction

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10.29220/CSAM.2022.29.5.615

Cite this

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title = "Intensive comparison of semi-parametric and nonparametric dimension reduction methods in forward regression",

abstract = "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.",

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PY - 2022

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N2 - 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.

AB - 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.

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Intensive comparison of semi-parametric and nonparametric dimension reduction methods in forward regression

Abstract

Bibliographical note

Keywords

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