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A quantile based dimension reduction technique

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  • Aguilera Morillo, María del Carmen

Abstract

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 quantilebased 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.

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  • Aguilera Morillo, María del Carmen, 2021. "A quantile based dimension reduction technique," DES - Working Papers. Statistics and Econometrics. WS 33469, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:33469
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    References listed on IDEAS

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    1. Yadolah Dodge & Joe Whittaker, 2009. "Partial quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 35-57, June.
    2. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
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    Partial-Least-Squares;

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