Non-crossing parametric quantile functions: an application to extreme temperatures

• Main Authors: Sottile, Gianluca, Frumento, Paolo
• Other Authors: Arbia, G, Peluso, S, Pini, A, Rivellini, G, Sottile, G, Frumento, P
• Format: Book Part
• Language: English
• Published: Pearson 2019
• Subjects: Parametric quantile functions; quantile regression coefficients modelling (QRCM); R package qrcm; estimation of extremes; climate change.; Settore SECS-S/01 - Statistica; Arctic; Climate change
• Online Access: http://hdl.handle.net/10447/419560; https://it.pearson.com/content/dam/region-core/italy/pearson-italy/pdf/Dirigenti e istituzioni/ISTITUZIONI-HE-PDF-sis2019_V4.pdf

Quantile regression can be used to obtain a non-parametric estimate of a conditional quantile function. The presence of quantile crossing, however, leads to an invalid distribution of the response and makes it difficult to use the fitted model for prediction. In this work, we show that crossing can be alleviated by modelling the quantile function parametrically. We then describe an algorithm for constrained optimisation that can be used to estimate parametric quantile functions with the noncrossing property. We investigate climate change by modelling the long-term trends of extreme temperatures in the Arctic Circle.