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Application of Influence Function in Sufficient Dimension Reduction Models

Shrestha, Prabha
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1595278335591108

Abstract Details

2020, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
In regression analysis, sufficient dimension reduction (SDR) models have gained significant popularity in the past three decades. While many methods have been proposed in the literature regarding the analysis of SDR models, the vast majority are of the type called inverse regression methods, pioneered by the sliced inverse regression method (Li \cite{Li91}). Most of these inverse regression methods rely on a matrix, commonly known as the central matrix. One of the main goals of the analysis of SDR models is the estimation of the central space. An influence function (IF) is a tool that analyzes the performance of a statistical estimator. In this dissertation, we focus on the application of IF on the analysis of SDR models. There are various inverse regression methods in existence. But none of them stands out in all cases, and it is not clear which central matrix one should use out of numerous options existing in the literature. We propose an IF-based approach for selection of a best performing central matrix from a class of inverse regression methods, and we extend this approach to the situation where the data are partially contaminated. Asymptotic results are established, and an extensive simulation study is conducted to examine the performance of the proposed algorithm. Another issue in an SDR model is the estimation of the dimension of its central space. Based on the IF, we propose a measure that combines the eigenvalues of the central matrix and an IF measure to estimate the dimension of the central space. In addition, we analyze the IF of the functional of Benasseni's measure for a specific inverse regression method, the $k{\text-th}$ moment method.
Wei Lin (Advisor)
Rida Benhaddou (Committee Member)
Feng Yaqin (Committee Member)
Justin Holub (Committee Member)
132 p.
Mathematics; Statistics
Influence Function in Sufficient Dimension Reduction Models; Sufficient Dimension Reduction; Influence function; central subspace; central matrix; inverse regression methods; regression analysis

Recommended Citations

Citations

  • Shrestha, P. (2020). Application of Influence Function in Sufficient Dimension Reduction Models [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1595278335591108

    APA Style (7th edition)

  • Shrestha, Prabha. Application of Influence Function in Sufficient Dimension Reduction Models. 2020. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1595278335591108.

    MLA Style (8th edition)

  • Shrestha, Prabha. "Application of Influence Function in Sufficient Dimension Reduction Models." Doctoral dissertation, Ohio University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1595278335591108

    Chicago Manual of Style (17th edition)

ohiou1595278335591108
280
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This open access ETD is published by Ohio University and OhioLINK.