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ON PRINCIPAL GENERALIZED LINEAR MODELING FOR SUFFICIENT DIMENSION REDUCTION AND MODEL BUILDING
Zhao, Jiaxin
Zhao, Jiaxin
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Thesis/Dissertation
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2025-05
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https://doi.org/10.34944/qx2r-h510
Abstract
This dissertation develops a comprehensive framework for simultaneous sufficient dimension reduction (SDR) and model building based on the generalized linear model (GLM). Our main contribution are threefold. First, we propose the principal generalized linear model (PGLM) as a general-purpose SDR method. Next, we apply PGLM and its variation profile PGLM to fit the generalized single-index model. Last but not least, both the PGLM and profile PGLM are applied to fit the generalized partially linear single-index model. The effectiveness of our proposed methods are demonstrated through extensive simulation studies as well as two real data applications. The PGLM framework is very flexible, as it allows both the predictors and the responses to be either continuous or discrete. It is computationally inexpensive, as many existing GLM algorithms can be directly embedded in our new algorithms. Motivated by recent developments in parallel computing, we take a novel gradient-based approach for optimization. Extensions of our gradient-based algorithms for parallel computing are currently under investigation.
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