B1779
Title: Dimension reduction techniques based on quantiles
Authors: Alvaro Mendez Civieta - Universidad Carlos III de Madrid (Spain) [presenting]
M Carmen Aguilera-Morillo - Universitat Politecnica de Valencia (Spain)
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
Abstract: Partial least squares (PLS) is a well-known dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in collinear or high dimensional scenarios. Being based on OLS estimators, PLS is sensitive to the presence of outliers or heavy-tailed distributions. Opposed to this, quantile regression (QR) is a technique that provides estimates of the conditional quantiles of a response variable as a function of the covariates. The usage of the quantiles makes the estimates more robust against the presence of heteroscedasticity or outliers than OLS estimators. We introduce the fast partial quantile regression algorithm (fPQR), a quantile based technique that shares the main advantages of PLS: it is a dimension reduction technique that obtains uncorrelated scores maximizing the quantile covariance between predictors and responses. But additionally, it is also a robust, quantile linked methodology suitable for dealing with outliers, heteroscedastic or heavy-tailed datasets. The median estimator of the PQR algorithm is a robust alternative to PLS, while other quantile levels can provide additional information on the tails of the responses.
