Intensive numerical studies of optimal sufficient dimension reduction with singularity

Jae Keun Yoo; Da Hae Gwak; Min Sun Kim

doi:10.5351/CSAM.2017.24.3.303

Intensive numerical studies of optimal sufficient dimension reduction with singularity

Jae Keun Yoo, Da Hae Gwak, Min Sun Kim

Department of Statistics

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

Abstract

Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the X² test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

Original language	English
Pages (from-to)	303-315
Number of pages	13
Journal	Communications for Statistical Applications and Methods
Volume	24
Issue number	3
DOIs	https://doi.org/10.5351/CSAM.2017.24.3.303
State	Published - 1 May 2017

Bibliographical note

Funding Information:
For the corresponding author 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-2014R1A2A1A11049389 and 2009-0093827). For Da-Hae Gwak and Min-Sun Kim, this work was supported by the BK21 Plus Project through the National Research Foundation of Korea (NRF) funded by the Korean Ministry of Education (22A20130011003).

Publisher Copyright:
© 2017 The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.

Keywords

Chi-square test
Optimality
Singularity
Sufficient dimension reduction

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10.5351/CSAM.2017.24.3.303

Cite this

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title = "Intensive numerical studies of optimal sufficient dimension reduction with singularity",

abstract = "Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the X2 test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).",

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N2 - Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the X2 test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

AB - Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the X2 test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

KW - Chi-square test

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KW - Singularity

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Intensive numerical studies of optimal sufficient dimension reduction with singularity

Abstract

Bibliographical note

Keywords

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