Statistical Modelling 23 (2) (2023), 173195
Parametric estimation of non-crossing quantile
functions
Gianluca Sottile,
Department of Economics,
Business and Statistics,
University of Palermo,
Italy.
e-mail: gianluca.sottile@unipa.it
Paolo Frumento,
Department of Political Science,
University of Pisa,
Italy.
Abstract:
Quantile regression (QR) has gained popularity during the last decades, and is now considered
a standard method by applied statisticians and practitioners in various fields. In this work, we applied
QR to investigate climate change by analysing historical temperatures in the Arctic Circle. This approach
proved very flexible and allowed to investigate the tails of the distribution, that correspond to extreme
events. The presence of quantile crossing, however, prevented using the fitted model for prediction and
extrapolation. In search of a possible solution, we first considered a different version of QR, in which
the QR coefficients were described by parametric functions. This alleviated the crossing problem, but
did not eliminate it completely. Finally, we exploited the imposed parametric structure to formulate
a constrained optimization algorithm that enforced monotonicity. The proposed example showed
how the relatively unexplored field of parametric quantile functions could offer new solutions to the
long-standing problem of quantile crossing. Our approach is particularly convenient in situations, like
the analysis of time series, in which the fitted model may be used to predict extreme quantiles or to
perform extrapolation. The described estimator has been implemented in the R package qrcm.
Keywords:
parametric quantile functions, quantile regression coefficients modelling (QRCM), quantile
crossing; constrained optimization, R package qrcm
Downloads:
Supplementary material in zipped archive.
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