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On Analysis of Sufficient Dimension Reduction Models

An, Panduan
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1553705899416538

Abstract Details

2019, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
Sufficient dimension reduction in regression analysis has been one of the most popular topics in the past two decades. Sufficient dimension reduction is concerned with the situation where the conditional distribution of the response variable 𝑌 given the covariate vector 𝑋 depends on 𝑋 only through a set of linear combinations of 𝑋. This is known as sufficient dimension reduction (SDR) in the literature which aims at reducing the high dimension of covariates to avoid the so-called curse-of-dimensionality. One pioneering work in SDR is the sliced inverse regression (SIR) proposed by Li (1991). However, SIR is not exhaustive and in particular SIR works poorly when the regression function is nearly symmetric. In this dissertation, we propose a measurement of the monotonicity of the regression curve. An algorithm based on the measurement is developed to select an SDR method. Another key issue in regression analysis is variable selection. Most current methods in variable selection are penalty based. We propose a new method based on SSE ratio to identify significant variables that contribute to the SDR models. Relatively little work has been done for the comparison of two SDR models to our knowledge. We propose three test statistics for such comparison based on Mahalanobis distance, Bénasséni’s Coefficient, and nonparametric estimation of the regression function. Simulation studies have been conducted under various settings to demonstrate the performance of the proposed methods.
Wei Lin (Advisor)
Xiaoping Shen (Committee Member)
Rida Benhaddou (Committee Member)
Chulho Jung (Committee Member)
102 p.
Mathematics; Statistics
Sufficient dimension reduction; central subspace; central mean subspace; monotonicity; variable selection; hypothesis testing; nonparametric

Recommended Citations

Citations

  • An, P. (2019). On Analysis of Sufficient Dimension Reduction Models [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1553705899416538

    APA Style (7th edition)

  • An, Panduan. On Analysis of Sufficient Dimension Reduction Models. 2019. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1553705899416538.

    MLA Style (8th edition)

  • An, Panduan. "On Analysis of Sufficient Dimension Reduction Models." Doctoral dissertation, Ohio University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1553705899416538

    Chicago Manual of Style (17th edition)

ohiou1553705899416538
388
© 2019, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.