Dimension reduction techniques for conditional expectiles

Marginalizing the importance of characterizing tail events can lead to catastrophic repercussions. Look no further than examples from meteorology and climatology (polar reversals, natural disasters), economics (2008 subprime mortgage crisis), or even medical-diagnostics (low/high risk patients in survival analysis). Investigating these events can become even more challenging when working with high-dimensional data, making it necessary to use dimension reduction techniques. Although research has recently turned to dimension reduction techniques that use conditional quantiles, there is a surprisingly limited amount of research dedicated to the underexplored research area of expectile regression (ER). Therefore, we present the first comprehensive work about dimension reduction techniques for conditional expectiles. Specifically, we introduce the central expectile subspace, i.e., the space that spans the fewest linear combinations of the predictors that contain all the information about the response that is available from the conditional expectile. We then introduce a nonlinear extension of the proposed methodology that extracts nonlinear features. The performance of the algorithms are demonstrated through extensive simulation examples and a real data application. The results suggest that ER is an effective tool for describing tail events and is a competitive alternative to quantile regression.