Fast partial quantile regression Articles uri icon

publication date

  • April 2022

volume

  • 223

International Standard Serial Number (ISSN)

  • 0169-7439

Electronic International Standard Serial Number (EISSN)

  • 1873-3239

abstract

  • (copyright) 2022 Elsevier B.V.Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantile based estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example.

keywords

  • dimension-reduction; outliers; partial-least-squares; quantile-regression; robust