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Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

Stochastic environmental research and risk assessment, 2018-11, Vol.32 (11), p.3207-3225 [Peer Reviewed Journal]

The Author(s) 2018 ;Stochastic Environmental Research and Risk Assessment is a copyright of Springer, (2018). All Rights Reserved. © 2018. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 1436-3240 ;EISSN: 1436-3259 ;DOI: 10.1007/s00477-018-1573-6

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Title:
Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes
Author: Cannon, Alex J.
Subjects: Annual rainfall ; Aquatic Pollution ; Chemistry and Earth Sciences ; Climatic data ; Computational Intelligence ; Computer Science ; Computer simulation ; Constraint modelling ; Data processing ; Earth and Environmental Science ; Earth Sciences ; Economic models ; Environment ; Environmental science ; Estimates ; Math. Appl. in Environmental Science ; Mathematical models ; Neural networks ; Nonlinear equations ; Original Paper ; Physics ; Probability Theory and Stochastic Processes ; Quantiles ; Rain ; Rainfall intensity ; Regression analysis ; Regression models ; Statistical analysis ; Statistics for Engineering ; Storms ; Waste Water Technology ; Water Management ; Water Pollution Control
Is Part Of: Stochastic environmental research and risk assessment, 2018-11, Vol.32 (11), p.3207-3225
Description: The goal of quantile regression is to estimate conditional quantiles for specified values of quantile probability using linear or nonlinear regression equations. These estimates are prone to “quantile crossing”, where regression predictions for different quantile probabilities do not increase as probability increases. In the context of the environmental sciences, this could, for example, lead to estimates of the magnitude of a 10-year return period rainstorm that exceed the 20-year storm, or similar nonphysical results. This problem, as well as the potential for overfitting, is exacerbated for small to moderate sample sizes and for nonlinear quantile regression models. As a remedy, this study introduces a novel nonlinear quantile regression model, the monotone composite quantile regression neural network (MCQRNN), that (1) simultaneously estimates multiple non-crossing, nonlinear conditional quantile functions; (2) allows for optional monotonicity, positivity/non-negativity, and generalized additive model constraints; and (3) can be adapted to estimate standard least-squares regression and non-crossing expectile regression functions. First, the MCQRNN model is evaluated on synthetic data from multiple functions and error distributions using Monte Carlo simulations. MCQRNN outperforms the benchmark models, especially for non-normal error distributions. Next, the MCQRNN model is applied to real-world climate data by estimating rainfall Intensity–Duration–Frequency (IDF) curves at locations in Canada. IDF curves summarize the relationship between the intensity and occurrence frequency of extreme rainfall over storm durations ranging from minutes to a day. Because annual maximum rainfall intensity is a non-negative quantity that should increase monotonically as the occurrence frequency and storm duration decrease, monotonicity and non-negativity constraints are key constraints in IDF curve estimation. In comparison to standard QRNN models, the ability of the MCQRNN model to incorporate these constraints, in addition to non-crossing, leads to more robust and realistic estimates of extreme rainfall.
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
Language: English
Identifier: ISSN: 1436-3240
EISSN: 1436-3259
DOI: 10.1007/s00477-018-1573-6
Source: Springer Nature OA/Free Journals
ProQuest Central

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Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes

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