B1869
Title: Regularized partial least squares for extreme values
Authors: Stephane Girard - Inria (France)
Hadrien Lorenzo - University Aix Marseille (France) [presenting]
Julyan Arbel - Inria (France)
Abstract: The focus is within the context of the dimension reduction for conditional extreme values. More specifically, the focus is on the case where the extreme values of a response variable may be explained by non-linear functions of some linear projections of the input random vector. The estimation of the projection directions has been investigated in the extreme-PLS (EPLS) method, an adaptation of the original PLS method to the extreme-value framework. A new interpretation of the EPLS direction is introduced as a maximum likelihood estimator based on the von Mises-Fisher distribution on hyperballs. The Bayesian paradigm then makes it possible to introduce prior information on the dimension reduction direction. The maximum a posteriori estimator is derived in two particular cases and interpreted as a shrinkage of the EPLS estimator. Its asymptotic behavior is established as the sample size tends to infinity. A simulated data study shows that the proposed method is effective for moderate data problems in high-dimensional settings. An illustration of the effectiveness of the proposed method is provided on French farm income data from which 259 dimensions have been considered in the descriptor.
