Shrinkage for Extreme Partial Least-Squares
HAL (Le Centre pour la Communication Scientifique Directe)(2024)
摘要
This work focuses on dimension-reduction techniques for modelling conditional
extreme values. Specifically, we investigate the idea that extreme values of a
response variable can be explained by nonlinear functions derived from linear
projections of an input random vector. In this context, the estimation of
projection directions is examined, as approached by the Extreme Partial Least
Squares (EPLS) method–an adaptation of the original Partial Least Squares
(PLS) method tailored to the extreme-value framework. Further, a novel
interpretation of EPLS directions as maximum likelihood estimators is
introduced, utilizing the von Mises-Fisher distribution applied to hyperballs.
The dimension reduction process is enhanced through the Bayesian paradigm,
enabling the incorporation of prior information into the projection direction
estimation. The maximum a posteriori estimator is derived in two specific
cases, elucidating it as a regularization or shrinkage of the EPLS estimator.
We also establish its asymptotic behavior as the sample size approaches
infinity. A simulation data study is conducted in order to assess the practical
utility of our proposed method. This clearly demonstrates its effectiveness
even in moderate data problems within high-dimensional settings. Furthermore,
we provide an illustrative example of the method's applicability using French
farm income data, highlighting its efficacy in real-world scenarios.
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关键词
least squares
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