Unstructured principal fitted response reduction in multivariate regression

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Abstract

In this paper, an unstructured principal fitted response reduction approach is proposed. The new approach is mainly different from two existing model-based approaches, because a required condition is assumed in a covariance matrix of the responses instead of that of a random error. Also, it is invariant under one of popular ways of standardizing responses with its sample covariance equal to the identity matrix. According to numerical studies, the proposed approach yields more robust estimation than the two existing methods, in the sense that its asymptotic performances are not severely sensitive to various situations. So, it can be recommended that the proposed method should be used as a default model-based method.

Original languageEnglish
Pages (from-to)561-567
Number of pages7
JournalJournal of the Korean Statistical Society
Volume48
Issue number4
DOIs
StatePublished - Dec 2019

Bibliographical note

Funding Information:
The author is grateful to the associate editor and the two reviewers for many insightful and helpful comments. The author also appreciates Professor Junhui Wang in School of Data Science and Department of Mathematics, City University of Hong Kong to provide helpful comments and suggestions to complete the manuscript during a visit in July, 2018. 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-2017R1A2B1004909 ).

Funding Information:
The author is grateful to the associate editor and the two reviewers for many insightful and helpful comments. The author also appreciates Professor Junhui Wang in School of Data Science and Department of Mathematics, City University of Hong Kong to provide helpful comments and suggestions to complete the manuscript during a visit in July, 2018. 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-2017R1A2B1004909).

Publisher Copyright:
© 2019 The Korean Statistical Society

Keywords

  • Model-based reduction
  • Multivariate regression
  • Response dimension reduction
  • Sufficient dimension reduction

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