Parametric estimation of non-crossing quantile functions

被引:7
|
作者
Sottile, Gianluca [1 ]
Frumento, Paolo [2 ]
机构
[1] Univ Palermo, Dept Econ Business & Stat, Via E Basile,Bldg 13, I-90128 Palermo, Italy
[2] Univ Pisa, Dept Polit Sci, Pisa, Italy
关键词
parametric quantile functions; Quantile regression coefficients modelling (QRCM); quantile crossing; constrained optimization; R packageQRcm; REGRESSION; TEMPERATURE; TRENDS; PRECIPITATION; EFFICIENT; CURVES; SERIES;
D O I
10.1177/1471082X211036517
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
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.
引用
收藏
页码:173 / 195
页数:23
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