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Activity Number:
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32
- Nonparametric Methods with High-Dimensional Data
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Type:
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Contributed
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Date/Time:
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Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #320770
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Title:
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On Forward Sufficient Dimension Reduction for Categorical and Ordinal Responses
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Author(s):
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Harris Quach* and Bing Li
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Companies:
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Pennsylvania State University and Penn State University
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Keywords:
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Central Mean Space;
K-mean clustering;
Multivariate Generalized Linear Model;
Outer Product of Gradients
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Abstract:
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We introduce a forward sufficient dimension reduction method for categorical or ordinal responses by extending the outer product of gradients and minimum average variance estimator to categorical and ordinal-categorical generalized linear models. Previous works in this direction extend forward regression to binary responses, and are applied in a pairwise manner for multi-category data, which is less efficient than our approach. Like other forward regression-based sufficient dimension reduction methods, our approach avoids the relatively stringent distributional requirements necessary for inverse regression alternatives. We show the consistency of our proposed estimator and derive its convergence rate. We develop an algorithm for our methods based on repeated applications of available algorithms for forward regression. We also propose a clustering-based tuning procedure to estimate the bandwidth. The effectiveness of our estimator and related algorithms is demonstrated via simulations and applications.
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Authors who are presenting talks have a * after their name.
