Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Censored Composite Conditional Quantile Screening for High-Dimensional Survival Data

In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.

Estimation of speed-related car body acceleration limits with quantile regression

Purpose–This study aimed to facilitate a rapid evaluation of track service status and vehicle ride comfort based on car body acceleration.Consequently,a low-cost,data-driven approach was proposed for analyzing speed-related acceleration limits in metro systems.Design/methodology/approach–A portable sensing terminal was developed to realize easy and efficient detection of car body acceleration.Further,field measurements were performed on a 51.95-km metro line.Data from 272 metro sections were tested as a case study,and a quantile regression method was proposed to fit the control limits of the car body acceleration at different speeds using the measured data.Findings–First,the frequency statistics of the measured data in the speed-acceleration dimension indicated that the car body acceleration was primarily concentrated within the constant speed stage,particularly at speeds of 15.4,18.3,and 20.9 m/s.Second,resampling was performed according to the probability density distribution of car body acceleration for different speed domains to achieve data balance.Finally,combined with the traditional linear relationship between speed and acceleration,the statistical relationships between the speed and car body acceleration under different quantiles were determined.We concluded the lateral/vertical quantiles of 0.8989/0.9895,0.9942/0.997,and 0.9998/0.993 as being excellent,good,and qualified control limits,respectively,for the lateral and vertical acceleration of the car body.In addition,regression lines for the speedrelated acceleration limits at other quantiles(0.5,0.75,2s,and 3s)were obtained.Originality/value–The proposed method is expected to serve as a reference for further studies on speedrelated acceleration limits in rail transit systems.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

Do U.S.economic conditions at the state level predict the realized volatility of oil‑price returns?A quantile machine‑learning approach

Because the U.S.is a major player in the international oil market,it is interesting to study whether aggregate and state-level economic conditions can predict the subse-quent realized volatility of oil price returns.To address this research question,we frame our analysis in terms of variants of the popular heterogeneous autoregressive realized volatility(HAR-RV)model.To estimate the models,we use quantile-regression and quantile machine learning(Lasso)estimators.Our estimation results highlights the dif-ferential effects of economic conditions on the quantiles of the conditional distribution of realized volatility.Using weekly data for the period April 1987 to December 2021,we document evidence of predictability at a biweekly and monthly horizon.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

一个基于Quantile估计的电容层析成像图像重建算法

电容层析成像图像重建是一个典型的病态问题,它的解是不稳定的。为了获得有意义的重建结果,能够保证解的稳定性而又能提高重建图像质量的方法应该被采用。本文提出了一个新的电容层析成像图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态特点利用Quantile估计和加权l_p范数构建扩展的目标泛函,将图像重建问题转化为一个最优化问题;在此基础上用Newton法求解该泛函。数值实验表明该算法是可行的,能够有效克服ECT图像重建的数值不稳定性。就本文所考察的重建对象而言,该法所重建图像的空间分辨率得到了提高。而且该算法计算直接、无需任何复杂的技巧,从而为ECT图像重建提供了一种有效的方法。

市场化、FDI与内资企业技术创新——基于Quantile方法的实证研究

本文利用2006—2010年中国大中型工业企业省际面板数据,运用Quantile方法对我国市场化改革过程中的FDI技术溢出机制进行了较为细致的分析。实证结果发现:在控制了市场化因素情况下,FDI对内资企业的技术创新的影响并不显著;国内市场环境的改善能促进FDI技术溢出效率,同时FDI也能促进国内市场环境的改善,但是这种相互作用只有在内资企业技术创新的0.5—0.75分位数时才最明显。

Quantile Trends in Temperature Extremes in China

A number of recent studies have examined trends in extreme temperature indices using a linear regression model based on ordinary least-squares. In this study, quantile regression was, for the first time, applied to examine the trends not only in the mean but also in all parts of the distribution of several extreme temperature indices in China for the period 1960–2008. For China as a whole, the slopes in almost all the quantiles of the distribution showed a notable increase in the numbers of warm days and warm nights, and a significant decrease in the number of cool nights. These changes became much faster as the quantile increased. However, although the number of cool days exhibited a significant decrease in the mean trend estimated by classical linear regression, there was no obvious trend in the upper and lower quantiles. This finding suggests that examining the trends in different parts of the distribution of the time-series is of great importance. The spatial distribution of the trend in the 90 th quantile indicated that there was a pronounced increase in the numbers of warm days and warm nights, and a decrease in the number of cool nights for most of China, but especially in the northern and western parts of China, while there was no significant change for the number of cool days at almost all the stations.

Volatile Compounds Selection via Quantile Correlation and Composite Quantile Correlation: A Whiting Case Study

The freshness and quality indices of whiting (Merlangius merlangus) influenced by a large number of chemical volatile compounds, are here analyzed in order to select the most relevant compounds as predictors for these indices. The selection process was performed by means of recent statistical variable selection methods, namely robust model-free feature screening, based on quantile correlation and composite quantile correlation. On the one hand, compounds 2-Methyl-1-butanol, 3-Methyl-1-butanol, Ethanol, Trimethylamine, 3-Methyl butanal, 2-Methyl-1-propanol, Ethylacetate, 1-Butanol and 2,3-Butanedione were identified as major predictors for the freshness index and on the other hand, compounds 3-Methyl-1-butanol, 2-Methyl-1- butanol, Ethanol, 3-Methyl butanal, 3-Hydroxy-2-butanone, 1-Butanol, 2,3-Butane- dione, 3-Pentanol, 3-Pentanone and 2-Methyl-1-propanol were identified as major predictors for the quality index.

Using Quantile Regression Approach to Analyze Price Movements of Agricultural Products in China

This paper studies how the price movements of pork,chicken and egg respond to those of related cost factors in short terms in Chinese market.We employ a linear quantile approach not only to explore potential data heteroscedasticity but also to generate confidence bands for the purpose of price stability study.We then evaluate our models by comparing the prediction intervals generated from the quantile regression models with in-sample and out-of-sample forecasts.Using monthly data from January 2000 to October 2010,we observed these findings：（i） the price changes of cost factors asymmetrically and unequally influence those of the livestock across different quantiles;（ii） the performance of our models is robust and consistent for both in-sample and out-of-sample forecasts;（iii） the confidence intervals generated from 0.05th and 0.95th quantile regression models are good methods to forecast livestock price fluctuation.

Impact of the COVID‑19 outbreak on the US equity sectors:Evidence from quantile return spillovers

The aim of this study is to examine the extreme return spillovers among the US stock market sectors in the light of the COVID-19 outbreak.To this end,we extend the now-traditional Diebold-Yilmaz spillover index to the quantiles domain by building networks of generalized forecast error variance decomposition of a quantile vector autoregressive model specifically for extreme returns.Notably,we control for common movements by using the overall stock market index as a common factor for all sectors and uncover the effect of the COVID-19 outbreak on the dynamics of the network.The results show that the network structure and spillovers differ considerably with respect to the market state.During stable times,the network shows a nice sectoral clustering structure which,however,changes dramatically for both adverse and beneficial market conditions constituting a highly connected network structure.The pandemic period itself shows an interesting restructuring of the network as the dominant clusters become more tightly connected while the rest of the network remains well separated.The sectoral topology thus has not collapsed into a unified market during the pandemic.

Some recent developments in modeling quantile treatment effects

This paper provides a selective review of the recent developments on econometric/statistical modeling in quantile treatment effects under both selection on observables and on unobservables.First,we discuss identification,estimation and inference of quantile treatment effects under the framework of selection on observables.Then,we consider the case where the treatment variable is endogenous or self-selected,for which an instrumental variable method provides a powerful tool to tackle this problem.Finally,some extensions are discussed to the data-rich environments,to the regression discontinuity design,and some other approaches to identify quantile treatment effects are also discussed.In particular,some future research works in this area are addressed.

Using Quantile Regression to Detect Relationships between Large-scale Predictors and Local Precipitation over Northern China

Quantile regression（QR） is proposed to examine the relationships between large-scale atmospheric variables and all parts of the distribution of daily precipitation amount at Beijing Station from 1960 to 2008. QR is also applied to evaluate the relationship between large-scale predictors and extreme precipitation（90th quantile） at 238 stations in northern China.Finally, QR is used to fit observed daily precipitation amounts for wet days at four sample stations. Results show that meridional wind and specific humidity at both 850 h Pa and 500 h Pa（V850, SH850, V500, and SH500） strongly affect all parts of the Beijing precipitation distribution during the wet season（April–September）. Meridional wind, zonal wind, and specific humidity at only 850 h Pa（V850, U850, SH850） are significantly related to the precipitation distribution in the dry season（October–March）. Impacts of these large-scale predictors on the daily precipitation amount with higher quantile become stronger, whereas their impact on light precipitation is negligible. In addition, SH850 has a strong relationship with wet-season extreme precipitation across the entire region, whereas the impacts of V850, V500, and SH500 are mainly in semi-arid and semi-humid areas. For the dry season, both SH850 and V850 are the major predictors of extreme precipitation in the entire region. Moreover, QR can satisfactorily simulate the daily precipitation amount at each station and for each season, if an optimum distribution family is selected. Therefore, QR is valuable for detecting the relationship between the large-scale predictors and the daily precipitation amount.

A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA

A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

Bayesian regularized quantile regression:A robust alternative for genome-based prediction of skewed data

Genomic prediction(GP)has become a valuable tool for predicting the performance of selection candidates for the next breeding cycle.A vast majority of statistical linear models on which GP is based rely on the assumption of normality of the residuals and therefore on the response variable itself.In this study,we propose to use Bayesian regularized quantile regression(BRQR)in the context of GP;the model has been successfully used in other research areas.We evaluated the prediction ability of the proposed model and compared it with the Bayesian ridge regression(BRR;equivalent to genomic best linear unbiased predictor,GBLUP).In addition,BLUP can be used with pedigree information obtained from the coefficient of coancestry(ABLUP).We have found that the prediction ability of BRQR is comparable to that of BRR and,in some cases,better;it also has the potential to efficiently deal with outliers.A program written in the R statistical package is available as Supplementary material.

QUANTILE ESTIMATION WITH AUXILIARY INFORMATION UNDER POSITIVELY ASSOCIATED SAMPLES

The empirical likelihood is used to propose a new class of quantile estimators in the presence of some auxiliary information under positively associated samples. It is shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators.

A PRELIMINARY STUDY ON COMBINING TWO KINDS OF PROXY DATA USING THE CONDITIONAL QUANTILE ADJUSTMENT METHOD

Based on two kinds of proxy data, a tree-ring width chronology at Huashan and the wetness/dryness grade series around Xi'an in north-centralChina, thes presat study demonstrates how different types of proxy climaterecords can be combined to give a more reliable estimate of past climate thaneither record can be done individually. With comparison and correction of thetwo data sets, various statistical models can be developed from individual andcombined senes. Among them, the best combined model produced by theconditional quantile adjustmat method can be selected for reconstruction ofApril-July rainfall at Huashan back to 1600 A.D.

Penalized Flexible Bayesian Quantile Regression

The selection of predictors plays a crucial role in building a multiple regression model. Indeed, the choice of a suitable subset of predictors can help to improve prediction accuracy and interpretation. In this paper, we propose a flexible Bayesian Lasso and adaptive Lasso quantile regression by introducing a hierarchical model framework approach to enable exact inference and shrinkage of an unimportant coefficient to zero. The error distribution is assumed to be an infinite mixture of Gaussian densities. We have theoretically investigated and numerically compared our proposed methods with Flexible Bayesian quantile regression (FBQR), Lasso quantile regression (LQR) and quantile regression (QR) methods. Simulations and real data studies are conducted under different settings to assess the performance of the proposed methods. The proposed methods perform well in comparison to the other methods in terms of median mean squared error, mean and variance of the absolute correlation criterions. We believe that the proposed methods are useful practically.