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arXiv · 1909.11948

Dynamic Partial Sufficient Dimension Reduction

Lu Li·Kai Tan·Xuerong Meggie Wen·Zhou Yu
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Abstract

Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when the predictors naturally fall into two sets, X and W, and we seek dimension reduction on X alone while considering all predictors in the regression analysis. Though partial dimension reduction is a very general problem, only very few research results are available when W is continuous. To the best of our knowledge, these methods generally perform poorly when X and W are related, furthermore, none can deal with the situation where the reduced lower-dimensional subspace of X varies dynamically with W. In this paper, We develop a novel dynamic partial dimension reduction method, which could handle the dynamic dimension reduction issue and also allows the dependency of X on W. The asymptotic consistency of our method is investigated. Extensive numerical studies and real data analysis show that our {\it Dynamic Partial Dimension Reduction} method has superior performance comparing to the existing methods.

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Lu Li, Kai Tan, Xuerong Meggie Wen, Zhou Yu. 2019-09-26. Dynamic Partial Sufficient Dimension Reduction. https://arxiv.org/abs/1909.11948

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