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Flexible parametric quantile regression model

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Abstract

This article introduces regression quantile models using both RS (Ramberg and Schmeiser, Commun Assoc Comput Mach 17:78–82, 1974) and FKML (Freimer et al., Commun Stat 17(10):3547–3567, 1988) generalised lambda distributions (GLD) and demonstrates the versatility of proposed models for a range of linear/non-linear and heteroscedastic/homoscedastic empirical data. Owing to the rich shapes of GLDs, GLD quantile regression is a competitive flexible model compared to standard quantile regression. The proposed method has some major advantages: (1) it provides a reference line which is very robust to outliers with the attractive property of zero mean residuals and (2) it gives a unified, elegant quantile regression model from the reference line with smooth regression coefficients across different quantiles. The proposed method has wide applications given the flexibility of GLDs. The goodness of fit of the proposed model can be assessed via QQ plots and the Kolmogorov–Smirnov test, to ensure the appropriateness of the statistical inference under consideration.

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  1. Covance Pty Ltd., Sydney, Floor 3, 4 Research Park Drive, Macquarie Park, NSW , 2113, Australia

    Steve Su

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Su, S. Flexible parametric quantile regression model. Stat Comput 25, 635–650 (2015). https://doi.org/10.1007/s11222-014-9457-1

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  • DOI: https://doi.org/10.1007/s11222-014-9457-1

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