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.

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.

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.

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.

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.

An Empirical Analysis of Employment Stability and the Wage Gap of Rural Migrants in China Based on Quantile Regression

Under the background of accelerated integrated urban-rural development, this paper offers an analysis on the short-term employment of rural migrants in China and resulting wage gap between long-term and short-term rural migrants. On the basis of correcting for sample selection problems arising from labor market participation and short-term employment, rural migrants＇ wage function is estimated using quantile regression method, and wage gap between long-term and short-term rural migrants is decomposed using MM method. Our empirical results suggest that those with a higher level of education, training experience and local employment recommended by family relations or in formal labor market are more likely to secure long-term labor contract,＂ region and education have significant contributions to the wage of rural migrants,＂ rural migrants of both long- and short-term contract types have great gaps at the bottom of salary distribution; and there exists a sticky floor effect in wage difference of rural migrants. These results have important policy implications in enhancing employment stability of rural migrants, improving income distribution equity, speeding up the process of urbanization, and balancing regional development.

Probabilistic Quantile Regression-Based Scour Estimation Considering Foundation Widths and Flood Conditions

Scour has been widely accepted as a key reason for bridge failures.Bridges are susceptible and sensitive to the scour phenomenon,which describes the loss of riverbed sediments around the bridge supports because of flow.The carrying capacity of a deep-water foundation is influenced by the formation of a scour hole,which means that a severe scour can lead to a bridge failure without warning.Most of the current scour predictions are based on deterministic models,while other loads at bridges are usually provided as probabilistic values.To integrate scour factors with other loads in bridge design and research,a quantile regression model was utilized to estimate scour depth.Field data and experimental data from previous studies were collected to build the model.Moreover,scour estimations using the HEC-18 equation and the proposed method were compared.By using the“CCC(Calculate,Confirm,and Check)”procedure,the probabilistic concept could be used to calculate various scour depths with the targeted likelihood according to a specified chance of bridge failure.The study shows that with a sufficiently large and continuously updated database,the proposed model could present reasonable results and provide guidance for scour mitigation.

Study on Rice Yield Estimation Model Based on Quantile Regression

An airborne multi-spectral camera was used in this study to estimate rice yields.The experimental data were achieved by obtaining a multi-spectral image of the rice canopy in an experimental field throughout the jointing stage(July,2017)and extracting five vegetation indices.Vegetation indices and rice growth parameter data were compared and analyzed.Effective predictors were screened by using significance analysis and quantile and ordinary least square(OLS)regression models estimating rice yields were constructed.The results showed that a quantile regression model based on normalized difference vegetation indices(NDVI)and rice yields performed was best forτ=0.7 quantile.Thus,NDVI was determined as an effective variable for the rice yield estimation during the jointing stage.The accuracy of the quantile regression estimation model was then assessed using RMES and MAPE test indicators.The yields by this approach had better results than those of an OLS regression estimation model and showed that quantile regression had practical applications and research significance in rice yields estimation.

Quantile Regression Analysis on Sex Wage Difference

Based on the investigation data of social position of national women in the third phase by National Women's Federation and National Bureau of Statistics in 2010,regression analysis on sex wage difference is conducted. It is divided into two parts. The first part is the impact on wage by sex,and it is divided into whole country,eastern,central and western regions. The second part is the impact on wage by different education backgrounds. It tries to explore sex wage difference situation at different positions of wage distribution,study if there exists " ceiling effect" or " floor effect" in population's wage distribution situation,sex wage difference situation in eastern,central and western regions and the education's impact on future income situations of men and women.

Interpersonal Climate Change Communication in Florida Using Quantile Regression

Climate change is described as a potentially catastrophic phenomenon with the capacity to disrupt agricultural production, economies, health systems, education, and infrastructure, among other systems. In Florida, climate change is a concern because of the state’s extensive coastline and its influence on the economy, as well as residents’ safety and well-being. As early as 2007, researchers forecasted that vulnerable wetlands, mangroves, fisheries, and coastal infrastructure in Florida may be significantly damaged or destroyed by 2060. Climate change communication (CCC) is described as a complex problem that requires several layers of attention, especially in achieving the desired outcome of behavior change. Previous research suggested that climate change communicators would be more effective if they understood their audiences and their communication capacities. The purpose of the study was to determine the impact of demographic factors on social communication for residents of Florida. A survey was used to collect the data through an address-based sampling (ABS) method, where a total of 318 usable responses were received from Florida residence 18 years or older. A latent construct for describing social communication (Social Communication Index [SCI]) was created as the dependent variable and was tested against eight variables using a quantile regression approach. Using quantiles in 0.1 intervals, the results showed that knowledge, age, income, newspaper use, urbanicity, and race affected the SCI in one or more quantiles. Social media, sex, and religiosity were insignificant throughout all quantiles. While most of the results align with previous research, there is the need for further probing into social communication on climate change to ensure that audience segments are provided with climate change information through the channels they primarily use.

A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.

Jackknife Model Averaging for Composite Quantile Regression

In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.

Height-diameter models for King Boris fir(Abies borisii regis Mattf.) and Scots pine(Pinus sylvestris L.) in Olympus and Pieria Mountains, Greece

In forest science and practice, the total tree height is one of the basic morphometric attributes at the tree level and it has been closely linked with important stand attributes. In the current research, sixteen nonlinear functions for height prediction were tested in terms of their fitting ability against samples of Abies borisii regis and Pinus sylvestris trees from mountainous forests in central Greece. The fitting procedure was based on generalized nonlinear weighted regression. At the final stage, a five-quantile nonlinear height-diameter model was developed for both species through a quantile regression approach, to estimate the entire conditional distribution of tree height, enabling the evaluation of the diameter impact at various quantiles and providing a comprehensive understanding of the proposed relationship across the distribution. The results clearly showed that employing the diameter as the sole independent variable, the 3-parameter Hossfeld function and the 2-parameter N?slund function managed to explain approximately 84.0% and 81.7% of the total height variance in the case of King Boris fir and Scots pine species, respectively. Furthermore, the models exhibited low levels of error in both cases(2.310m for the fir and 3.004m for the pine), yielding unbiased predictions for both fir(-0.002m) and pine(-0.004m). Notably, all the required assumptions for homogeneity and normality of the associated residuals were achieved through the weighting procedure, while the quantile regression approach provided additional insights into the height-diameter allometry of the specific species. The proposed models can turn into valuable tools for operational forest management planning, particularly for wood production and conservation of mountainous forest ecosystems.

The Short-Term Prediction ofWind Power Based on the Convolutional Graph Attention Deep Neural Network

The fluctuation of wind power affects the operating safety and power consumption of the electric power grid and restricts the grid connection of wind power on a large scale.Therefore,wind power forecasting plays a key role in improving the safety and economic benefits of the power grid.This paper proposes a wind power predicting method based on a convolutional graph attention deep neural network with multi-wind farm data.Based on the graph attention network and attention mechanism,the method extracts spatial-temporal characteristics from the data of multiple wind farms.Then,combined with a deep neural network,a convolutional graph attention deep neural network model is constructed.Finally,the model is trained with the quantile regression loss function to achieve the wind power deterministic and probabilistic prediction based on multi-wind farm spatial-temporal data.A wind power dataset in the U.S.is taken as an example to demonstrate the efficacy of the proposed model.Compared with the selected baseline methods,the proposed model achieves the best prediction performance.The point prediction errors(i.e.,root mean square error(RMSE)and normalized mean absolute percentage error(NMAPE))are 0.304 MW and 1.177%,respectively.And the comprehensive performance of probabilistic prediction(i.e.,con-tinuously ranked probability score(CRPS))is 0.580.Thus,the significance of multi-wind farm data and spatial-temporal feature extraction module is self-evident.

Does China's digital economy contribute to low-carbon transition?

The digital economy,as a new emerging economic form,has become an important power for realizing Chinese-style modernization and promoting green development in China.This paper measures the digital economy and low-carbon transition index based on the data of 30 provinces in China from 2013 to 2020 and analyzes the mechanism and path of the digital economy affecting low-carbon transition using the fixed effect panel data model and the threshold effect model.It is found that,(1)The digital economy and low-carbon transition in China are various in different regions,with characteristics of being unbalanced and insufficient.(2)The digital economy significantly promotes low-carbon transition,with the greatest influence in the Central region,followed by the Eastern region and the Western region.Under different dimensions,the development of informatization and digital transactions promote low-carbon transition,but the development of the internet plays an inhibiting role.(3)The higher the degree of urbanization and environmental regulation,the greater the influence of the digital economy on low-carbon transition.

The k Nearest Neighbors Estimator of the M-Regression in Functional Statistics

It is well known that the nonparametric estimation of the regression function is highly sensitive to the presence of even a small proportion of outliers in the data.To solve the problem of typical observations when the covariates of the nonparametric component are functional,the robust estimates for the regression parameter and regression operator are introduced.The main propose of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed processes fully automatic.We use thek Nearest Neighbors procedure(kNN)to construct the kernel estimator of the proposed robust model.Under some regularity conditions,we state consistency results for kNN functional estimators,which are uniform in the number of neighbors(UINN).Furthermore,a simulation study and an empirical application to a real data analysis of octane gasoline predictions are carried out to illustrate the higher predictive performances and the usefulness of the kNN approach.

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.

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.

An Efficient Smooth Quantile Boost Algorithm for Binary Classification

In this paper, we propose a Smooth Quantile Boost Classification (SQBC) algorithm for binary classification problem. The SQBC algorithm directly uses a smooth function to approximate the “check function” of the quantile regression. Compared to other boost-based classification algorithms, the proposed algorithm is more accurate, flexible and robust to noisy predictors. Furthermore, the SQBC algorithm also can work well in high dimensional space. Extensive numerical experiments show that our proposed method has better performance on randomly simulations and real data.

L1/2 -Regularized Quantile Method for Sparse Phase Retrieval

The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L1/2-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.