Semiparametric quantile regression using family of quantile-based asymmetric densities

• Published in: Computational Statistics & Data Analysis
• Main Authors: Gijbels, Irene, KARIM, Rezaul, VERHASSELT, Anneleen
• Format: Article in Journal/Newspaper
• Language: English
• Published: ELSEVIER 2021
• Subjects: Asymptotic distribution; Bandwidth selection; Local likelihood; Local polynomial fitting; North Atlantic
• Online Access: http://hdl.handle.net/1942/33968; https://doi.org/10.1016/j.csda.2020.107129

Quantile regression is an important tool in data analysis. Linear regression, or more generally, parametric quantile regression imposes often too restrictive assumptions. Nonparametric regression avoids making distributional assumptions, but might have the disadvantage of not exploiting distributional modelling elements that might be brought in. A semiparametric approach towards estimating conditional quantile curves is proposed. It is based on a recently studied large family of asymmetric densities of which the location parameter is a quantile (and not a mean). Passing to conditional densities and exploiting local likelihood techniques in a multiparameter functional setting then leads to a semiparametric estimation procedure. For the local maximum likelihood estimators the asymptotic distributional properties are established, and it is discussed how to assess finite sample bias and variance. Due to the appealing semiparametric framework, one can discuss in detail the bandwidth selection issue, and provide several practical bandwidth selectors. The practical use of the semiparametric method is illustrated in the analysis of maximum winds speeds of hurricanes in the North Atlantic region, and of bone density data. A simulation study includes a comparison with nonparametric local linear quantile regression as well as an investigation of robustness against miss-specifying the parametric model part. (C) 2020 Elsevier B.V. All rights reserved. The authors thank an Associate Editor and reviewers for their valuable comments which led to a considerable improvement of the manuscript. The authors gratefully acknowledge support from the Research Foundation - Flanders, Belgium (FWO research project G.0826.15N). The first and second authors acknowledge support of the GOA project GOA/12/014 of the Research Council KU Leuven, Belgium. The third author is grateful for the support from the Research Foundation Flanders, Belgium (FWO research grant 1518917N), and from the Special Research Fund (Bijzonder Onderzoeksfonds) of ...