Quantile Score Research Articles

Specification Choices in Quantile Regression for Empirical Macroeconomics

ABSTRACTQuantile regression has become widely used in empirical macroeconomics, in particular for estimating and forecasting tail risks. This paper examines various choices in the specification of quantile regressions for macro applications, including how and to what extent to include shrinkage and whether to apply shrinkage in a classical or Bayesian framework. We focus on forecasting accuracy, measured with quantile scores and quantile‐weighted continuous ranked probability scores at a range of quantiles from the left to right tail. Across applications, we find that shrinkage is generally helpful to quantile forecast accuracy, with Bayesian quantile regression dominating frequentist quantile regression.JEL Classification: C53, E17, E37, F47

A novel hybrid model based on evolving multi-quantile long and short-term memory neural network for ultra-short-term probabilistic forecasting of photovoltaic power

Probabilistic forecasting is extremely crucial in eliminating uncertainty in photovoltaic (PV) power generation. Quantile regression long and short-term memory neural network (QRLSTM) is widely recognized as promising methods for PV power probabilistic forecasting due to their strong generalization ability. However, these models train the model for each quantile individually, which lacks consideration of the correlation and monotonicity between quantiles, and multiple training leads to excessive computational complexity. Furthermore, the non-differentiable pinball loss function generated by QR places significant demands on the optimization algorithms. To address these issues, this paper proposes an evolutive distributed chaotic particle swarm optimization (EDCPSO)-optimized multi-quantile LSTM (MQLSTM) to achieve high-quality probabilistic PV power prediction. MQLSTM is a multi-output network structure that simultaneously outputs all quantile estimates and adopts a loss function with all quantile scores and non-crossing constraints to guide the training of the model. This approach not only improves the quality and reasonableness of quantile estimations, but also reduces computational difficulty. Then, from the perspective of evolutionary computation, considering the weight parameters of each connection layer in MQLSTM as decision variables, we convert the probabilistic forecasting into an optimization problem and propose a EDCPSO to solve the training difficulty. It implements a targeted distributed chaos strategy based on the evolutionary state to improve convergence speed and search capability. The proposed model is tested to be superior in real cases.

A novel fatigue design modeling method under small-sample test data with generalized fiducial theory

Understanding the correlation between the fatigue life of engineering materials and the applied stress is a crucial aspect of reliability and safety design. However, small data observations frequently occur in fatigue testing due to factors like time and budget limitations, as well as constraints related to the availability of testing materials and resources. In this article, fiducial inference method is employed for modeling P-S-N curves to deal with scenarios with small sample sizes. Fiducial inference can be seen as a procedure that provides a measure within a parameter space while requiring fewer assumptions than Bayesian inference (no prior). The performance of the proposed method is evaluated by comparing it with the ISO method using statistical simulation data and aluminum alloy 2524-T3 data. In scenarios with ample data (no less than 15 observations at each of the four stress levels), the proposed fiducial-based method yields results comparable to those obtained through the ISO method. When dealing with small-sample data (around 2–4 observations for each of the four stress levels) and medium-sample data (about 5–10 observations per stress level), the proposed fiducial-based method consistently outperforms the ISO method in terms of the quantile scores (also known as pinball loss). This shows the advantageous performance of the fiducial method under conditions of limited data availability. Besides, the consistency in performance across varying data size scenarios underscores the reliability and robustness of the fiducial-based approach in estimating probabilistic S-N curves.

Real-time determination of moisture content of potato slices during drying using long short-term memory from image morphometric parameters

This article uses digital image processing to investigate the change in morphometric attributes of potato slices of 1 mm thickness for different drying temperatures (45, 50, 55 and 60 °C). For this purpose, a compact hot air dryer has been developed, having the desired provision for embedding an image acquisition system. The long short-term memory (LSTM) technique has been employed to determine the product moisture content inside the hot air dryer purely on the basis of morphometric characteristics of individual slices. The best-performing network optimized after hyperparameter tuning has an architecture of 156 hidden neurons, 2 LSTM units, and a learning rate of 0.0160. The optimized network’s training coefficient of determination (R2) and root mean square error (RMSE) are 0.977 and 0.0461, respectively. In addition, the quantitative uncertainty analysis using the quantile score (Q) and the prediction-interval-normalized root-mean-square width (PINRW) was carried out to evaluate the robustness of the network. This approach is instrumental in designing a non-invasive quality control system during drying phenomena. It also helps in studying the complexity of the drying mechanism by visualizing the morphometric changes taking place in the product during drying.

Density Forecast of Financial Returns Using Decomposition and Maximum Entropy

Abstract We consider a multiplicative decomposition of the financial returns to improve the density forecasts of financial returns. The multiplicative decomposition is based on the identity that financial return is the product of its absolute value and its sign. Advantages of modeling the two components are discussed. To reduce the effect of the estimation error due to the multiplicative decomposition in estimation of the density forecast model, we impose a moment constraint that the conditional mean forecast is set to match with the sample mean. Imposing such a moment constraint operates a shrinkage and tilts the density forecast of the decomposition model to produce the improved maximum entropy density forecast. An empirical application to forecasting density of the daily stock returns demonstrates the benefits of using the decomposition and imposing the moment constraint to obtain the improved density forecast. We evaluate the density forecast by comparing the logarithmic score (LS), the quantile score (QS), and the continuous ranked probability score (CRPS). We contribute to the literature on the density forecast and the decomposition models by showing that the density forecast of the decomposition model can be improved by imposing a sensible constraint in the maximum entropy framework.

ProteinLens: a web-based application for the analysis of allosteric signalling on atomistic graphs of biomolecules.

The investigation of allosteric effects in biomolecular structures is of great current interest in diverse areas, from fundamental biological enquiry to drug discovery. Here we present ProteinLens, a user-friendly and interactive web application for the investigation of allosteric signalling based on atomistic graph-theoretical methods. Starting from the PDB file of a biomolecule (or a biomolecular complex) ProteinLens obtains an atomistic, energy-weighted graph description of the structure of the biomolecule, and subsequently provides a systematic analysis of allosteric signalling and communication across the structure using two computationally efficient methods: Markov Transients and bond-to-bond propensities. ProteinLens scores and ranks every bond and residue according to the speed and magnitude of the propagation of fluctuations emanating from any site of choice (e.g. the active site). The results are presented through statistical quantile scores visualised with interactive plots and adjustable 3D structure viewers, which can also be downloaded. ProteinLens thus allows the investigation of signalling in biomolecular structures of interest to aid the detection of allosteric sites and pathways. ProteinLens is implemented in Python/SQL and freely available to use at: www.proteinlens.io.

Explanation and Probabilistic Prediction of Hydrological Signatures with Statistical Boosting Algorithms

Hydrological signatures, i.e., statistical features of streamflow time series, are used to characterize the hydrology of a region. A relevant problem is the prediction of hydrological signatures in ungauged regions using the attributes obtained from remote sensing measurements at ungauged and gauged regions together with estimated hydrological signatures from gauged regions. The relevant framework is formulated as a regression problem, where the attributes are the predictor variables and the hydrological signatures are the dependent variables. Here we aim to provide probabilistic predictions of hydrological signatures using statistical boosting in a regression setting. We predict 12 hydrological signatures using 28 attributes in 667 basins in the contiguous US. We provide formal assessment of probabilistic predictions using quantile scores. We also exploit the statistical boosting properties with respect to the interpretability of derived models. It is shown that probabilistic predictions at quantile levels 2.5% and 97.5% using linear models as base learners exhibit better performance compared to more flexible boosting models that use both linear models and stumps (i.e., one-level decision trees). On the contrary, boosting models that use both linear models and stumps perform better than boosting with linear models when used for point predictions. Moreover, it is shown that climatic indices and topographic characteristics are the most important attributes for predicting hydrological signatures.

QUANTILE PROBABILITY PREDICTIONS: A DEMONSTRATIVE PERFORMANCE ANALYSIS OF FORECASTS OF US COVID-19 DEATHS

An analytical framework is presented for the evaluation of quantile probability forecasts. It is demonstrated using weekly quantile forecasts of changes in the number of US COVID-19 deaths. Empirical quantiles are derived using the assumption that daily changes in a variable follow a normal distribution with time varying means and standard deviations, which can be assumed constant over short horizons such as one week. These empirical quantiles are used to evaluate quantile forecasts using the Mean Squared Quantile Score (MSQS), which, in turn, is decomposed into sub-components involving bias, resolution and error variation to identify specific aspects of performance, which highlight the strengths and weaknesses of forecasts. The framework is then extended to test if performance enhancement can be achieved by combining diverse forecasts from different sources. The demonstration illustrates that the technique can effectively evaluate quantile forecasting performance based on a limited number of data points, which is crucial in emergency situations such as forecasting pandemic behavior. It also shows that combining the predictions with quantile probability forecasts generated from an Autoregressive Order One, AR(1) model provided substantially improved performance. The implications of these findings are discussed, suggestions are offered for future research and potential limitations are considered.

Quantile regression averaging‐based probabilistic forecasting of daily ambient temperature

AbstractThe inclusion of conductor temperature variations for numerous power system planning and operational studies has long been recognized in the literature. The conductor temperature is majorly affected by environmental factors such as the ambient temperature. An efficient forecasting technique for forecasting ambient temperature is the need of the hour to prevent unexpected hazards in power systems and other areas caused due to temperature variations. Numerous researches have proposed different point forecasting and probabilistic forecasting models for the forecasting of ambient temperature. The probabilistic forecasting of ambient temperature provides complete information about future uncertainties, therefore quantifying the effects of daily temperature variations. A forecast combination approach, such as the quantile regression averaging, has never been utilized in this context. The selection of suitable point forecasters that complement each other's effects by characterizing different aspects of the ambient temperature data for averaging and the use of frequency components that explain the daily and periodic seasonal variations of ambient temperature to construct a forecasting model are the significant features of this paper. The proposed model is used with four varieties, and each is compared with the others. It is found that the variant using all the complementary individual point forecasters performs better in making probabilistic forecasts than the other options as well as better than the popular quantile k‐nearest neighbors, quantile egression forests, and basic quantile regression as inferred from the quantile score, Winkler score, and reliability plots.

Ensemble solar forecasting using data-driven models with probabilistic post-processing through GAMLSS

Forecast performance of data-driven models depends on the local weather and climate regime, which makes model selection a tedious task for forecast practitioners. Ensemble forecasting, or forecast combination, is beneficial in such cases, in that, forecasts from multiple models are combined to form a final forecast. In ensemble forecasting, additional to the final deterministic-style forecasts, predictive distributions are also available, which can be used by grid operators for better decision-making. Such empirical predictive distributions are useful to represent the uncertainty associated with the forecasts. However, raw ensemble forecasts are often not calibrated, e.g., due to the lack of diversity in the ensemble members. The lack of ensemble spread is known as underdispersion, and it can be ameliorated through post-processing.This study aims to calibrate hourly ensemble clear-sky index forecasts, generated by 20 data-driven models, using both parametric and nonparametric post-processing techniques. Four years of data collected at 7 research-grade sites are used in the empirical part of the paper. Quantitative and qualitative methods are used to evaluate the performance of post-processing techniques in terms of calibration and sharpness. Post-processed ensemble forecasts outperform raw ensemble forecasts under all verification metrics. The proposed parametric post-processing technique, namely, generalized additive models for location, scale and shape, substantially reduces the continuous ranked probability score (CRPS) of the raw ensemble forecasts from 32–59 W/m2 to 25–45 W/m2 and quantile score from 16–30 W/m2 to 13–23 W/m2. In terms of CRPS skill score, the proposed method achieved 38–58% improvements over a climatology reference.

Forecasting conditional extreme quantiles for wind energy

Probabilistic forecasting of distribution tails (i.e., quantiles below 0.05 and above 0.95) is challenging for non-parametric approaches since data for extreme events are scarce. A poor forecast of extreme quantiles can have a high impact in various power system decision-aid problems. An alternative approach more robust to data sparsity is extreme value theory (EVT), which uses parametric functions for modelling distribution’s tails. In this work, we apply conditional EVT estimators to historical data by directly combining gradient boosting trees with a truncated generalized Pareto distribution. The parametric function parameters are conditioned by covariates such as wind speed or direction from a numerical weather predictions grid. The results for a wind power plant located in Galicia, Spain, show that the proposed method outperforms state-of-the-art methods in terms of quantile score.

Testing linearity in partial functional linear quantile regression model based on regression rank scores

This paper investigates the hypothesis test of the parametric component in partial functional linear quantile regression model in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. A quantile rank score test based on functional principal component analysis is developed. Under mild conditions, we establish the consistency of the proposed test statistic, and show that the proposed test can detect Pitman local alternatives converging to the null hypothesis at the usual parametric rate. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, an illustrative example is given through fitting the Berkeley growth data and testing the effect of gender on the height of kids.

OC26.06: A new diagnostic way in fetuses with tetralogy of Fallot based on the normal fetal quantile score data model

OC26.06: A new diagnostic way in fetuses with tetralogy of Fallot based on the normal fetal quantile score data model

Assessment of school readiness of children and factors associated with risk of inadequate school readiness in Ujjain, India: an observational study

ObjectiveSchool readiness is a condition or state indicating that the child is ready to learn in a formal educational set-up. The objective of this study was to estimate the prevalence...

Constrained Quantile Regression Splines for Ensemble Postprocessing

Abstract Statistical postprocessing of ensemble forecasts is widely applied to make reliable probabilistic weather forecasts. Motivated by the fact that nature imposes few restrictions on the shape of forecast distributions, a flexible quantile regression method based on constrained spline functions (CQRS) is proposed and tested on ECMWF Ensemble Prediction System (ENS) wind speed forecasting data at 125 stations in Norway. First, it is demonstrated that constraining quantile functions to be monotone and bounded is preferable. Second, combining an ensemble quantile with the ensemble mean proved to be a good covariate for the respective quantile. Third, CQRS only needs to be applied to about 10 equidistant quantiles, while those between can be obtained by interpolation. A comparison of CQRS versus a mixture model of truncated and lognormal distributions showed slight overall improvements in quantile score (less than 1%), reliability, and to some extent also sharpness. For strong wind speed forecasts the quantile score was improved by up to 4.5% depending on lead time.

Does More Managerial Power Impede or Promote Corporate Tax Avoidance? Evidence from Listed Chinese Companies

Paying taxes is a form of corporate social responsibility. Corporate tax avoidance effectively reduces operating costs, thereby increasing shareholder returns, but the pros and cons are different for executives. This paper takes data from companies listed in China from 2000 to 2016 to explore the causal relationship between managerial power and corporate tax avoidance, using principal component analysis and entropy weight methodology to construct managerial power. First, we conduct an ordinary least square regression, and then we employ alternative measures to avoid taxation, and use managerial power as a robustness check. Next, we rerun the model by using quantile regression and propensity score matching. Finally, in order to tackle problems with endogeneity, we carry out regressions utilizing instrumental variables and simultaneous regression equations. We conclude that managerial power reduces corporate tax avoidance, and firms with more managerial power have fewer incentives to avoid taxes. The results of this paper can guide the taxation of companies listed on the Chinese market to achieve the full payment of tax obligations by reinforcing managerial power in companies, which improves national taxation and leads to sustained economic growth.

Quantile Score: A New Reference System for Quantitative Fetal Echocardiography Based on a Large Multicenter Study

Normative ranges of fetal echocardiographic measurements are important for quantitative diagnosis of fetal cardiovascular disease. The current normative ranges were derived from small samples and were based on the hypothesis of a normal distribution of these measurements during fetal cardiovascular growth. The aims of this study were to test the hypothesis of a normal distribution of fetal echocardiographic measurements in a large multicenter cohort and to propose a reference system without the normal distribution hypothesis to improve accuracy of fetal echocardiographic measurements. Fifty-two variables from 6,343 normal fetal echocardiographic examinations were acquired from seven Chinese centers. The hypothesis of a normal distribution used in ordinary least squares regression was tested with the Jarque-Bera test. The quantile score (q score) derived from quantile regression without normal distribution hypothesis was compared with the Z score derived from ordinary least squares regression. A total of 288 fetuses with outflow tract and great artery abnormalities and 300 normal fetuses were used to compare the diagnostic accuracy of q and Z scores. All fetal echocardiographic measurements showed non-normal distributions (P<.001). The normal range was underestimated by ordinary least squares regression compared with quantile regression by 30±11%. The partial normalized areas under the receiver operating characteristic curve within the 20% false-positive rate were 0.62 and 0.50 for the q and Z scores, respectively. The q score provides a more robust system for determining normative ranges of fetal echocardiographic measurements. The improved sensitivity of matched false-positive rates makes the q score a more accurate reference for prenatal diagnosis, assessment, and prognosis of fetal cardiovascular disease.

Neural networks for GEFCom2017 probabilistic load forecasting

This report describes the forecasting model which was developed by team “4C” for the global energy forecasting competition 2017 (GEFCom2017), with some modifications added afterwards to improve its accuracy. The model is based on neural networks. Temperature scenarios obtained from historical data are used as inputs to the neural networks in order to create load scenarios, and these load scenarios are then transformed into quantiles. By using a feature selection approach that is based on a stepwise regression technique, a neural network based model is developed for each zone. Furthermore, a dynamic choice of the temperature scenarios is suggested. The feature selection and dynamic choice of the temperature scenarios can improve the quantile scores considerably, resulting in very accurate forecasts among the top teams.

Ensemble size: How suboptimal is less than infinity?

Ensemble forecasts are the method of choice in numerical weather prediction (NWP) to generate probabilistic forecasts. The number of members in an ensemble is an important factor in determining how well a probability distribution of a weather‐related variable can be estimated. Having only a finite number of members reduces the average skill such a probabilistic forecast can have. Increasing ensemble size is therefore desirable; however, ensemble size is also proportional to the computational cost. Having a small ensemble size limits the cost and makes other improvements, such as increases in spatial resolution, feasible.This article examines how average skill measures with metrics such as the continuous ranked probability score, the quantile score, and the Dawid–Sebastiani score converge with ensemble size. A numerical experiment with a 200 member ensemble using the European Centre for Medium‐Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) model at a resolution of 29 km and a forecast range of 15 days provides data to compare the convergence of probabilistic skill in a current NWP system with theoretical expectations derived for perfectly reliable ensembles with exchangeable members.Results in the first part of the article can help users of operational NWP ensemble forecasts formulate their minimum requirement in terms of ensemble size. In the second part, requirements for scientists who test changes to NWP systems are examined. Using proper scores and fair scores, it is explored whether testing changes in the ensemble forecasts can be meaningful with fewer members than in the operational configuration. Results are based on medium‐range numerical experiments with 50 members. Two experiments test the activation of a representation of model uncertainty and three other experiments test changes in horizontal resolution from 29 to 18 km and from 29 to 45 km.

Benthic invertebrate taxonomic and trait associations with land use in an intensively managed watershed: Implications for indicator identification

Expansion and intensification of human land uses has resulted in the loss of all but remnant areas of natural cover over increasingly vast areas of land. Effective stream assessment in these regions thus requires indicators sensitive to ecosystem change in systems that are already highly stressed. The goal of this study was to determine if benthic macroinvertebrate communities in streams exposed to extensive anthropogenic stress are associated with land-use variables and demonstrate potential to be used as bioindicators for assessment of further land use modification. Using the Grand River in southern Ontario as our model, we sampled for benthic macroinvertebrates in 70 small (3–20 km2) sub-watersheds that comprised a gradient of intensive land use (65–100% developed). Redundancy analysis and variance partitioning results indicated that macroinvertebrate taxonomy and traits were only weakly associated with environmental gradients with the strongest associations occurring at the reach scale. With strong anthropogenic filters present across the watershed, it is likely that the majority of benthic macroinvertebrate communities in the Grand River have experienced a homogenization towards tolerant taxa and traits that respond more to local habitat variables. Threshold Indicator Taxa Analysis (TITAN) revealed 19 valid taxa indicators and 32 valid trait indicators for one or more of six environmental variables (percent sub-watershed agriculture, percent buffer agriculture, pool substrate, sediment reduction, natural channel, and riparian width). However, individual taxon and community change points exhibited broad quantile scores indicating a gradual or random response to environmental variables. Comparison of traits and taxonomic associations with environmental variables showed minimal difference suggesting traits may not offer increased sensitivity to land-use stress. However, several traits did show potential to serve as diagnostic indicators for specific stressors associated with agricultural land use. Our ability to identify even a few indicators in a region with intensive human activity is promising for land managers charged with detecting biotic alterations in this stressed system. Further research developing indicators sensitive to intensification of anthropogenic stress in extensively developed landscapes is critical to ensuring managers have the tools needed to protect and enhance aquatic resources.