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.

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 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.

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.

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.

Does the Digital Economy Optimize Tourism Industry Structure?Effects and Mechanisms Based on Quantile Regression and Threshold Modeling

A comprehensive evaluation index system is constructed,and the entropy weight TOPSIS method isused to measure the optimization level of the digital economy and tourism industry structure of 30 provinces inChina from 2012 to 2021.Moreover,models such as quantile regression and panel threshold are used to explorethe influence of the digital economy(DIG)on the optimization of the tourism industry structure(TIS)as well as itstransmission mechanism.The study reveals that DIG significantly promotes TIS,which remains valid after endogeneity and robustness tests;the impact of DIG on TIS exhibited a“U-shape”effect that first decreases and thenincreases,and its highest significance is at the 90%quartile level.Threshold model tests revealed a nonlinearthreshold effect with DIG and tourism total factor productivity(TTFP)as a single threshold and tourism technological progress index(TECH)as a double threshold,and the second threshold has the largest effect of 0.163.Mechanism analysis found that the mediating impact of the DIG on the TIS was mediated by increasing the TTFP,and the TECH accounted for the highest proportion of 12.15%.Regional analysis revealed that the role of DIG onthe TIS is Central>East>West>Northeast,and the empowering effect is more significant in the high digital economylevel area and the high tourism industry structure optimization area.

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.

Variable selection via quantile regression with the process of Ornstein-Uhlenbeck type

Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.

A Frisch-Newton Algorithm for Sparse Quantile Regression

Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large empirical applications, the design matrix has a verysparse structure. A typical example is the classical fixed-effect model for panel data where theparametric dimension of the model can be quite large, but the number of non-zero elements is quitesmall. Adopting recent developments in sparse linear algebra we introduce a modified version of theFrisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28]. The newalgorithm substantially reduces the storage (memory) requirements and increases computational speed.The modified algorithm also facilitates the development of nonparametric quantile regressionmethods. The pseudo design matrices employed in nonparametric quantile regression smoothing areinherently sparse in both the fidelity and roughness penalty components. Exploiting the sparsestructure of these problems opens up a whole range of new possibilities for multivariate smoothingon large data sets via ANOVA-type decomposition and partial linear models.

Quantile Regression for Right-Censored and Length-Biased Data

Length-biased data arise in many important fields, including epidemiological cohort studies, cancer screening trials and labor economics. Analysis of such data has attracted much attention in the literature. In this paper we propose a quantile regression approach for analyzing right-censored and length-biased data. We derive an inverse probability weighted estimating equation corresponding to the quantile regression to correct the bias due to length-bias sampling and informative censoring. This method can easily handle informative censoring induced by length-biased sampling. This is an appealing feature of our proposed method since it is generally difficult to obtain unbiased estimates of risk factors in the presence of length-bias and informative censoring. We establish the consistency and asymptotic distribution of the proposed estimator using empirical process techniques. A resampling method is adopted to estimate the variance of the estimator. We conduct simulation studies to evaluate its finite sample performance and use a real data set to illustrate the application of the proposed method.

Partial functional linear quantile regression

This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.

Performance Improvement of Very Short-term Prediction Intervals for Regional Wind Power Based on Composite Conditional Nonlinear Quantile Regression

Accurate regional wind power prediction plays an important role in the security and reliability of power systems.For the performance improvement of very short-term prediction intervals(PIs),a novel probabilistic prediction method based on composite conditional nonlinear quantile regression(CCNQR)is proposed.First,the hierarchical clustering method based on weighted multivariate time series motifs(WMTSM)is studied to consider the static difference,dynamic difference,and meteorological difference of wind power time series.Then,the correlations are used as sample weights for the conditional linear programming(CLP)of CCNQR.To optimize the performance of PIs,a composite evaluation including the accuracy of PI coverage probability(PICP),the average width(AW),and the offsets of points outside PIs(OPOPI)is used to quantify the appropriate upper and lower bounds.Moreover,the adaptive boundary quantiles(ABQs)are quantified for the optimal performance of PIs.Finally,based on the real wind farm data,the superiority of the proposed method is verified by adequate comparisons with the conventional methods.

A Longitudinal Study of the Effects of Family Background Factors on Mathematics Achievements Using Quantile Regression

Quantile regression is gradually emerging as a powerful tool for estimating models of conditional quantile functions, and therefore research in this area has vastly increased in the past two decades. This paper, with the quantile regression technique, is the first comprehensive longitudinal study on mathematics participation data collected in Alberta, Canada. The major advantage of longitudinal study is its capability to separate the so-called cohort and age effects in the context of population studies. One aim of this paper is to study whether the family background factors alter performance on the mathematical achievement of the strongest students in the same way as that of weaker students based on the large longitudinal sample of 2000, 2001 and 2002 mathematics participation longitudinal data set. The interesting findings suggest that there may be differential family background factor effects at different points in the mathematical achievement conditional distribution.

Double Penalized Quantile Regression for the Linear Mixed Effects Model

This paper proposes a double penalized quantile regression for linear mixed effects model,which can select fixed and random effects simultaneously.Instead of using two tuning parameters,the proposed iterative algorithm enables only one optimal tuning parameter in each step and is more efficient.The authors establish asymptotic normality for the proposed estimators of quantile regression coefficients.Simulation studies show that the new method is robust to a variety of error distributions at different quantiles.It outperforms the traditional regression models under a wide array of simulated data models and is flexible enough to accommodate changes in fixed and random effects.For the high dimensional data scenarios,the new method still can correctly select important variables and exclude noise variables with high probability.A case study based on a hierarchical education data illustrates a practical utility of the proposed approach.